{"id":703,"date":"2016-11-29T12:25:10","date_gmt":"2016-11-29T03:25:10","guid":{"rendered":"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/?p=703"},"modified":"2026-01-28T09:49:20","modified_gmt":"2026-01-28T00:49:20","slug":"%e7%b5%90%e5%90%88%e9%98%bb%e5%ae%b3%e5%ae%9a%e6%95%b0ki%e3%81%ae%e8%a8%88%e7%ae%97%e5%bc%8f%e3%81%ab%e3%81%a4%e3%81%84%e3%81%a6","status":"publish","type":"post","link":"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/2016\/11\/29\/%e7%b5%90%e5%90%88%e9%98%bb%e5%ae%b3%e5%ae%9a%e6%95%b0ki%e3%81%ae%e8%a8%88%e7%ae%97%e5%bc%8f%e3%81%ab%e3%81%a4%e3%81%84%e3%81%a6\/","title":{"rendered":"\u7d50\u5408\u963b\u5bb3\u5b9a\u6570Ki\u306e\u8a08\u7b97\u5f0f\u306b\u3064\u3044\u3066"},"content":{"rendered":"\n\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"508\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/munson_rodbard_2025-1024x508.png\" alt=\"\" class=\"wp-image-6743\" srcset=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/munson_rodbard_2025-1024x508.png 1024w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/munson_rodbard_2025-300x150.png 300w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/munson_rodbard_2025-768x381.png 768w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/munson_rodbard_2025-1536x762.png 1536w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/munson_rodbard_2025-2048x1016.png 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>In the world of drug discovery, where scientists are the detectives and diseases are the elusive criminals, radioligand binding assays (RLBAs) were once the Sherlock Holmes of the lab.<\/p>\n\n\n\n<p>\u2014 <a href=\"https:\/\/www.oncodesign-services.com\/cpt_ressource\/radioligand-binding-assays-a-lost-art-in-drug-discovery\/\" title=\"\">Ancellin, Nicolas, \u201cRadioligand Binding Assays: A Lost Art in Drug Discovery?\u201d.<\/a><\/p>\n<\/blockquote>\n\n\n\n<p>\u7814\u7a76\u5ba4\u5185\u5411\u3051\u30e1\u30e2\u3002December 24, 2025\u6539\u8a02\u3002<\/p>\n\n\n\n<p>\u7af6\u5408\u7d50\u5408\u8a66\u9a13\u306eIC<sub>50<\/sub>\u5024\u304b\u3089\u7d50\u5408\u963b\u5bb3\u5b9a\u6570\\(K_{\\rm i}\\)\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3068\u3057\u3066\u306f\u3001\u3088\u304f\u77e5\u3089\u308c\u3066\u3044\u308b\u8fd1\u4f3c\u7684\u306a<strong>Cheng&#8211;Prusoff\u5f0f<\/strong>\u306e\u4ed6\u306b\u3001\u53b3\u5bc6\u306a<strong>Munson&#8211;Rodbard\u5f0f<\/strong>\u304c\u3042\u308a\u307e\u3059\u3002\u307e\u305f\u3001IC<sub>50<\/sub>\u3092\u6c42\u3081\u308b\u65b9\u6cd5\u306b\u306f\u975e\u7dda\u5f62\u56de\u5e30\u3068\u7dda\u5f62\u56de\u5e30\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u65b9\u6cd5\u3067\u7d50\u5408\u963b\u5bb3\u5b9a\u6570\\(K_{\\rm i}\\)\u3092\u8a08\u7b97\u3057\u305f\u6642\u306b\u3001\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u306e\u771f\u306e\\(K_{\\rm i}\\)\u5024\u3068\u306e\u305a\u308c\u304c\u3069\u306e\u7a0b\u5ea6\u306a\u306e\u304b\u3092\u8abf\u3079\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p>\u8a08\u7b97\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306b\u306f\u53d7\u5bb9\u4f53\u3068\u3057\u3066\u30d7\u30ed\u30c6\u30a4\u30f3\u30ad\u30ca\u30fc\u30bcC \u03b4-C1B\u30c9\u30e1\u30a4\u30f3\u3001\u653e\u5c04\u6027\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u3068\u3057\u3066 [<sup>3<\/sup>H]phorbol 12,13-dibutyrate\uff08[<sup>3<\/sup>H]PDBu\uff09\u3092\u4f7f\u7528\u3057\u305f\u6642\u306e\u5178\u578b\u7684\u306a\u5024\u3092\u4f7f\u3044\u307e\u3057\u305f: \u53d7\u5bb9\u4f53\u7dcf\u6fc3\u5ea6\\([R]_{\\textrm T} = 3.45\\; \\textrm{nM}\\), \u653e\u5c04\u6027\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u7dcf\u6fc3\u5ea6\\([L]_{\\textrm T} = 17\\; \\textrm{nM}\\), \u653e\u5c04\u6027\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u306e\u53d7\u5bb9\u4f53\u306b\u5bfe\u3059\u308b\u89e3\u96e2\u5b9a\u6570\\(K_{\\textrm d} = 0.53\\; \\textrm{nM}\\)\u3002\u975e\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u306e\u6fc3\u5ea6\u7bc4\u56f2\u306f\u3001\\(K_{\\rm i}\\) = 0.05 nM\u306e\u6642log [<em>I<\/em>]<sub>T<\/sub> \u304c\u22129.021\u304b\u3089\u22127.457; 0.1 nM\u306e\u6642\u22129.172\u304b\u3089\u22127.459;  0.5 nM\u306e\u6642\u22128.908\u304b\u3089\u22126.987; 1 nM\u306e\u6642\u22128.454\u304b\u3089\u22126.496; 10 nM\u306e\u6642\u22127.495\u304b\u3089\u22125.500; 100 nM\u306e\u6642\u22126.500\u304b\u3089\u22124.500\u3067\u3059\uff0850%\u3092\u631f\u3080\u304a\u304a\u3088\u305d\u22120.5\u523b\u307f\u306e5\u70b9\uff09\u3002<\/p>\n\n\n\n<p>\u5f97\u3089\u308c\u308bIC<sub>50<\/sub>\u306e\u5024\u306f\u3001\u975e\u7dda\u5f62\u56de\u5e30\uff08\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u95a2\u6570\u3067\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\uff09\u3068\u7dda\u5f62\u56de\u5e30\u3068\u3067\u307b\u3068\u3093\u3069\u5dee\u306f\u3042\u308a\u307e\u305b\u3093\u3067\u3057\u305f\u3002<\/p>\n\n\n\n<figure class=\"wp-block-flexible-table-block-table is-style-stripes\"><table class=\"\"><tbody><tr><td style=\"border-color:#ffffff\"><strong>\u771f\u306e<em>K<\/em><sub>i<\/sub>\u5024<\/strong><\/td><td style=\"border-color:#ffffff\"><strong>[<em>I<\/em>]<sub>50<\/sub><\/strong> (nM)<\/td><td style=\"border-color:#ffffff\"><strong>\u771f\u306eIC<sub>50<\/sub><\/strong> (nM)<\/td><td style=\"border-color:#ffffff\"><strong>IC<sub>50<\/sub><\/strong> (\u975e\u7dda\u5f62\u56de\u5e30\u3001\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u95a2\u6570)<\/td><td style=\"border-color:#ffffff\"><strong>IC<sub>50<\/sub><\/strong> (\u7dda\u5f62\u56de\u5e30)<\/td><\/tr><tr><td style=\"border-color:#ffffff\">0.05 nM<\/td><td style=\"border-color:#ffffff\">1.51<\/td><td style=\"border-color:#ffffff\">3.24<\/td><td style=\"border-color:#ffffff\">3.18<\/td><td style=\"border-color:#ffffff\">3.17<\/td><\/tr><tr><td style=\"border-color:#ffffff\">0.1 nM<\/td><td style=\"border-color:#ffffff\">3.02<\/td><td style=\"border-color:#ffffff\">4.75<\/td><td style=\"border-color:#ffffff\">4.72<\/td><td style=\"border-color:#ffffff\">4.68<\/td><\/tr><tr><td style=\"border-color:#ffffff\">0.5 nM<\/td><td style=\"border-color:#ffffff\">15.1<\/td><td style=\"border-color:#ffffff\">16.8<\/td><td style=\"border-color:#ffffff\">16.8<\/td><td style=\"border-color:#ffffff\">16.8<\/td><\/tr><tr><td style=\"border-color:#ffffff\">1 nM<\/td><td style=\"border-color:#ffffff\">30.2<\/td><td style=\"border-color:#ffffff\">31.9<\/td><td style=\"border-color:#ffffff\">31.9<\/td><td style=\"border-color:#ffffff\">31.9<\/td><\/tr><tr><td style=\"border-color:#ffffff\">10 nM<\/td><td style=\"border-color:#ffffff\">302<\/td><td style=\"border-color:#ffffff\">304<\/td><td style=\"border-color:#ffffff\">303<\/td><td style=\"border-color:#ffffff\">303<\/td><\/tr><tr><td style=\"border-color:#ffffff\">100 nM<\/td><td style=\"border-color:#ffffff\">3019<\/td><td style=\"border-color:#ffffff\">3020<\/td><td style=\"border-color:#ffffff\">3015<\/td><td style=\"border-color:#ffffff\">3014<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-flexible-table-block-table is-style-stripes\"><table class=\"has-fixed-layout\"><tbody><tr><td rowspan=\"2\" style=\"border-color:#ffffff\"><strong>\u771f\u306e<em>K<\/em><sub>i<\/sub>\u5024<\/strong><\/td><td colspan=\"4\" style=\"border-color:#ffffff\"><strong>\u771f\u306eIC<sub>50<\/sub>\u304b\u3089\u8a08\u7b97\u3057\u305f<em>K<\/em><sub>i<\/sub>\u5024 (nM)<\/strong><\/td><\/tr><tr><td style=\"border-color:#ffffff\"><strong>Cheng&#8211;Prusoff<\/strong><\/td><td style=\"border-color:#ffffff\"><strong>Modified Cheng&#8211;Prusoff<\/strong><sup><em>a<\/em><\/sup><\/td><td style=\"border-color:#ffffff\"><strong>Munson&#8211;Rodbard (exact) correction<\/strong><\/td><td style=\"border-color:#ffffff\"><strong>IC<sub>50<\/sub> &#8211; [<em>R<\/em>]<sub>T<\/sub>\/2<\/strong> <strong>correction<\/strong><sup><em>b<\/em><\/sup><\/td><\/tr><tr><td style=\"border-color:#ffffff\">0.05 nM<\/td><td style=\"border-color:#ffffff\">0.0980<\/td><td style=\"border-color:#ffffff\">0.108<\/td><td style=\"border-color:#ffffff\">0.0500<\/td><td style=\"border-color:#ffffff\">0.0502<\/td><\/tr><tr><td style=\"border-color:#ffffff\">0.1 nM<\/td><td style=\"border-color:#ffffff\">0.143<\/td><td style=\"border-color:#ffffff\">0.159<\/td><td style=\"border-color:#ffffff\">0.100<\/td><td style=\"border-color:#ffffff\">0.100<\/td><\/tr><tr><td style=\"border-color:#ffffff\">0.5 nM<\/td><td style=\"border-color:#ffffff\">0.508<\/td><td style=\"border-color:#ffffff\">0.561<\/td><td style=\"border-color:#ffffff\">0.499<\/td><td style=\"border-color:#ffffff\">0.499<\/td><\/tr><tr><td style=\"border-color:#ffffff\">1 nM<\/td><td style=\"border-color:#ffffff\">0.964<\/td><td style=\"border-color:#ffffff\">1.07<\/td><td style=\"border-color:#ffffff\">1.00<\/td><td style=\"border-color:#ffffff\">1.00<\/td><\/tr><tr><td style=\"border-color:#ffffff\">10 nM<\/td><td style=\"border-color:#ffffff\">9.19<\/td><td style=\"border-color:#ffffff\">10.2<\/td><td style=\"border-color:#ffffff\">10.0<\/td><td style=\"border-color:#ffffff\">10.0<\/td><\/tr><tr><td style=\"border-color:#ffffff\">100 nM<\/td><td style=\"border-color:#ffffff\">91.3<\/td><td style=\"border-color:#ffffff\">101<\/td><td style=\"border-color:#ffffff\">100<\/td><td style=\"border-color:#ffffff\">100<\/td><\/tr><\/tbody><tfoot><tr><td colspan=\"5\" style=\"border-color:#ffffff\"><sup><em>a<\/em><\/sup>&nbsp;[<em>L<\/em>]<sub>T<\/sub>&nbsp;\u306e\u4ee3\u308f\u308a\u306b [<em>L<\/em>]<sub>50<\/sub>&nbsp;\u3092\u4f7f\u7528\u3057\u3066\u8a08\u7b97\u3057\u305f\u3002&nbsp;<br><em><sup>b<\/sup><\/em>&nbsp;\\(K_{\\mathrm i} = (\\mathrm{IC}_{50} &#8211; [R]_\\mathrm{T}\/2 )\/(2 [L]_{50}\/[L]_{0} &#8211; 1 + [L]_{50}\/K_\\mathrm{d}) \\).<\/td><\/tr><\/tfoot><\/table><\/figure>\n\n\n\n<p>\u5206\u304b\u3063\u305f\u3053\u3068:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\uff08\u30aa\u30ea\u30b8\u30ca\u30eb\u306e\uff09Cheng&#8211;Prusoff\u5f0f\u306f<em>K<\/em><sub>i<\/sub>\u5024\u304c\u9ad8\u3044\u6642\u306b\u3082\u610f\u5916\u306b\u305a\u308c\u304c\u5927\u304d\u3044\u3002<\/li>\n\n\n\n<li>[<em>L<\/em>]<sub>T<\/sub>\u306e\u4ee3\u308f\u308a\u306b [<em>L<\/em>]<sub>50<\/sub> \u3092\u4f7f\u3063\u305f\u4fee\u6b63Cheng&#8211;Prusoff\u5f0f\u306f\u3001<em>K<\/em><sub>i<\/sub> \u2267 10 nM\u306e\u5834\u5408\u306b\u771f\u306e<em>K<\/em><sub>i<\/sub>\u5024\u3068\u6709\u52b9\u6570\u5b572\u6841\u3067\u4e00\u81f4\u3059\u308b\u304c\u3001<em>K<\/em><sub>i<\/sub> \u304c\u4f4e\u3044\u6642\u306b\u306f\u305a\u308c\u304c\u5927\u304d\u3044\u3002<\/li>\n\n\n\n<li>\u8868\u8a08\u7b97\u30bd\u30d5\u30c8\u304c\u4f7f\u3048\u308b\u73fe\u5728\u3067\u306f\u53b3\u5bc6\u306aMunson\u2013Rodbard\u88dc\u6b63\u3092\u4f7f\u308f\u306a\u3044\u7406\u7531\u306f\u306a\u3044\u3002\u5c11\u306a\u304f\u3068\u3082 [<em>I<\/em>]<sub>50<\/sub> \u3068IC<sub>50<\/sub>\u306e\u5dee\u304c\u958b\u3044\u3066\u304f\u308b<em>K<\/em><sub>i <\/sub>&lt; 10 nM\u306e\u5834\u5408\u306f\u3001Munson&#8211;Rodbard\u5f0f\u3092\u4f7f\u3046\u5fc5\u8981\u304c\u3042\u308b\u3002<\/li>\n\n\n\n<li>IC<sub>50<\/sub> &#8211; [<em>R<\/em>]<sub>T<\/sub>\/2 \u88dc\u6b63\u3067\u306f\u7cbe\u5ea6\u7684\u306b\u306fMunson&#8211;Rodbard\u88dc\u6b63\u3068\u540c\u7b49\u3002<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u8a08\u7b97\u306b\u4f7f\u7528\u3059\u308b\u6570\u5024\u306eBinding assay\u304b\u3089\u306e\u7b97\u51fa\u65b9\u6cd5<\/h2>\n\n\n\n<p>Binding assay\u306e\u65b9\u6cd5\u306fSharkey &amp; Blumberg (1985) \u306b\u591a\u5c11\u306e\u5909\u66f4\u70b9\u3092\u52a0\u3048\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u5e73\u8861\u72b6\u614b\u3067\u306e\u975e\u7279\u7570\u7684\u7d50\u5408\u306f\u7121\u8996\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>Pellet (\u4e3b\u306b\u03b3\u30b0\u30ed\u30d6\u30ea\u30f3) \u306b\u5bfe\u3059\u308b\u975e\u7279\u7570\u7684\u5438\u7740\u3068\u4e0a\u6e05\u3068\u306e\u9593\u306e\u653e\u5c04\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u306e\u5206\u914d\u4fc2\u6570 <span style=\"font-weight: bold; font-style: italic;\">k<\/span> = [pellet<sub>(nonspecific)<\/sub>] \/ ([supernatant<sub>(nonspecific)<\/sub>] \u00d7 437\/50)<\/p>\n\n\n\n<p><span style=\"font-weight: bold;\">[<em>RL<\/em>]]<\/span> = [pellet<sub>(total)<\/sub>] \u2212 <span style=\"font-style: italic;\">k<\/span> \u00d7 [supernatant<sub>(total)<\/sub>] \u00d7 437\/50<\/p>\n\n\n\n<p><span style=\"font-weight: bold;\">[<em>L<\/em>]<sub>T<\/sub><\/span> = [pellet<sub>(total)<\/sub>] + [supernatant<sub>(total)<\/sub>] \u00d7 437\/50<\/p>\n\n\n\n<p><strong>[<em>L<\/em>]*<sub>T<\/sub><\/strong> = [<em>L<\/em>]<sub>T<\/sub>\/(1 + <em>k<\/em>)<\/p>\n\n\n\n<p><span style=\"font-weight: bold;\">[<em>L<\/em>]<sub>0<\/sub><\/span> = [supernatant<sub>(total)<\/sub>] = ([<em>L<\/em>]<sub>T<\/sub> \u2212 [<em>RL<\/em>]<sub>0<\/sub>)\/(1 + <em>k<\/em>)<\/p>\n\n\n\n<p><span style=\"font-weight: bold;\">[<em>L<\/em>]<sub>50<\/sub><\/span> = ([<em>L<\/em>]<sub>T<\/sub> \u2212 [<em>RL<\/em>]<sub>0<\/sub>\/2)\/(1 + <em>k<\/em>)<\/p>\n\n\n\n<p><span style=\"font-weight: bold;\">[<em>R<\/em>]<sub>T<\/sub><\/span> = <span style=\"font-style: italic;\">K<\/span><sub>d<\/sub> [<em>RL<\/em>]<sub>0<\/sub> \/ [<em>L<\/em>]<sub>0<\/sub> + [<em>RL<\/em>]<sub>0<\/sub><\/p>\n\n\n\n<p>\u653e\u5c04\u6d3b\u6027DPM\uff08\u58ca\u5909\u6bce\u5206\uff09\u3092\u30e2\u30eb\u6fc3\u5ea6 (nM) \u306b\u63db\u7b97\u3059\u308b\u4fc2\u6570<span style=\"font-style: italic;\">N<\/span>:<br>\\[<br>N = \\frac{1}{60} \\times \\frac{1}{3.7 \\times 10^{10}} \\times \\frac{1}{\\mbox{\u6bd4\u6d3b\u6027 (Ci\/mmol)}} \\times \\frac{1}{10^3} \\times \\frac{1}{250 \\times 10^{-6}} \\times 10^9<br>\\]\n\n\n\n<h3 class=\"wp-block-heading\">\u975e\u7279\u7570\u7684\u7d50\u5408\u306b\u3064\u3044\u3066<\/h3>\n\n\n\n<p>\u7d30\u80de\u306e\u819c\u753b\u5206\u3092binding assay\u306b\u7528\u3044\u308b\u5834\u5408\u3001\u819c\u30bf\u30f3\u30d1\u30af\u8cea\u3078\u306e\u4f4e\u89aa\u548c\u6027\u7d50\u5408\u3084\u30ea\u30f3\u8102\u8cea\u3078\u306e\u5206\u914d\u3001\u5206\u96e2\u30d5\u30a3\u30eb\u30bf\u30fc\u3078\u306e\u5438\u7740\u306a\u3069\u306e\u975e\u7279\u7570\u7684\u7d50\u5408\u304c\u8d77\u3053\u308b\u3002\u901a\u5e38\u3053\u308c\u3089\u306e\u4f4e\u89aa\u548c\u6027\u904e\u7a0b\u306f\u4e0d\u98fd\u548c\u3067\u3042\u308a\u3001\u975e\u7279\u7570\u7684\u7d50\u5408\u4fc2\u6570 (\\(k\\)) \u3068free\u653e\u5c04\u30ea\u30ac\u30f3\u30c9\u6fc3\u5ea6 \\([L]\\) \u306e\u7a4d\u3068\u3057\u3066\u30e2\u30c7\u30eb\u5316\u3067\u304d\u308b (Hulme and Trevethick, 2010)\u3002<\/p>\n\n\n\n[<sup>3<\/sup>H]PDBu\u7d50\u5408\u8a66\u9a13\u3067\u306f\u3001\u30dd\u30ea\u30a8\u30c1\u30ec\u30f3\u30b0\u30ea\u30b3\u30fc\u30eb (PEG) \u3092\u6dfb\u52a0\u3057\u3066\u30bf\u30f3\u30d1\u30af\u8cea\u3092\u51dd\u96c6\u3055\u305b\u307e\u3059\u304c\uff08PEG\u6c88\uff09\u3001\u5171\u6c88\u5264\u3068\u3057\u3066\u03b3-\u30b0\u30ed\u30d6\u30ea\u30f3\u3092\u7cfb\u306b\u52a0\u3048\u3066\u3044\u308b\u305f\u3081\u3001\u03b3-\u30b0\u30ed\u30d6\u30ea\u30f3\u306b\u5bfe\u3059\u308b\u975e\u7279\u7570\u7684\u5438\u7740\u304c\u8d77\u304d\u307e\u3059\uff08\u901a\u5e38\u5206\u914d\u4fc2\u6570 <em>k<\/em> = 3\u20135%\u7a0b\u5ea6\uff09\u3002\u3053\u306e\u975e\u7279\u7570\u7684\u5438\u7740\u304c [<em>RL<\/em>]<sub>0<\/sub> \u3068 [<em>L<\/em>]<sub>0<\/sub> \u306b\u3069\u306e\u7a0b\u5ea6\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u304b\u8a08\u7b97\u3057\u3066\u307f\u305f\u3068\u3053\u308d\u3001<em>k<\/em> = 0\u306e\u6642 <meta charset=\"utf-8\"> [<em>RL<\/em>]<sub>0<\/sub> = 3.321 nM\u3001[<em>L<\/em>]<sub>0<\/sub> = 13.7 nM\u3001<em>k<\/em> = 0.04\u306e\u6642 <meta charset=\"utf-8\"> [<em>RL<\/em>]<sub>0<\/sub> = 3.316 nM\u3001[<em>L<\/em>]<sub>0<\/sub> = 13.2 nM\u3067\u3057\u305f\u3002\u30ea\u30ac\u30f3\u30c9\u6fc3\u5ea6\u304c\u5341\u5206\u9ad8\u3051\u308c\u3070\u3001bound [<em>RL<\/em>] \u306b\u306f\u307b\u3068\u3093\u3069\u5f71\u97ff\u304c\u306a\u3044\u305f\u3081\u3001free [<em>L<\/em>] \u306e\u5024\u3060\u3051 <em>k<\/em> \u3067\u88dc\u6b63\u3059\u308c\u3070\u3088\u3044\u3067\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<p>\u975e\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u306e\u03b3-\u30b0\u30ed\u30d6\u30ea\u30f3\u306b\u5bfe\u3059\u308b\u975e\u7279\u7570\u7684\u7d50\u5408\u306b\u3064\u3044\u3066\u306f\u3001\u5206\u914d\u4fc2\u6570\u304c\u6e2c\u308c\u306a\u3044\u305f\u3081\u3001\u8003\u616e\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002\u4eee\u306b\u975e\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u306e\u03b3-\u30b0\u30ed\u30d6\u30ea\u30f3\u306b\u5bfe\u3059\u308b\u5206\u914d\u4fc2\u6570\u304c [<sup>3<\/sup>H]PDBu\u306e\u5206\u914d\u4fc2\u6570\u3068\u7b49\u3057\u3044\u3068\u3059\u308b\u3068\u3001\u52a0\u3048\u305f\u975e\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u306e\u6fc3\u5ea6\u3092 (1 + <em>k<\/em>) \u3067\u5272\u3063\u3066\u88dc\u6b63\u3059\u308b\u3053\u3068\u3067\u3001[<em>I<\/em>]<sub>T<\/sub>\u304c\u63a8\u5b9a\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u771f\u306e<em>K<\/em><sub>i<\/sub>\u304c10 nM\u306e\u30ea\u30ac\u30f3\u30c9\u306e\u5206\u914d\u4fc2\u6570 <em>k<\/em> = 0.04\u3068\u4eee\u5b9a\u3057\u305f\u5834\u5408\u3001Munson\u2013Rodbard\u5f0f\u3067\u8a08\u7b97\u3057\u305f<em>K<\/em><sub>i<\/sub>\u5024\u306f\u3001\u88dc\u6b63\u306a\u3057\u306710.47 nM\u3001\u88dc\u6b63\u3042\u308a\u306710.06 nM\u3067\u3057\u305f\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span style=\"font-weight: bold;\">Cheng\u2013Prusoff\u5f0f<\/span>\u306e\u5c0e\u51fa<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u4f7f\u7528\u3059\u308b\u30d1\u30e9\u30e1\u30fc\u30bf<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">Total binding\u7fa4<\/h4>\n\n\n\n<p>\\begin{equation}<br>[R]_0 + [L]_0 \\rightleftharpoons [RL]_0<br>\\end{equation}<br>\\begin{equation}<br>K_{\\rm d} = \\frac{[R]_0[L]_0}{[RL]_0}<br>\\end{equation}<br>\\begin{equation}<br>[R]_{\\rm T} = [R]_0 + [RL]_0<br>\\end{equation}<br>\\begin{equation}<br>K_{\\rm d} = \\frac{([R]_{\\rm T} &#8211; [RL]_0)[L]_0}{[RL]_0}<br>\\end{equation}<br>\\begin{equation}<br>[RL]_0 = \\frac{[R]_{\\rm T}[L]_0}{K_{\\rm d} + [L]_0}<br>\\end{equation}<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Competitive inhibition\u7fa4<\/h4>\n\n\n\n<p>\\([I]\\): \u904a\u96e2\u306e\u975e\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u6fc3\u5ea6<\/p>\n\n\n\n<p>\\begin{equation}<br>[RI] \\rightleftharpoons [I] + [R] + [L] \\rightleftharpoons [RL]<br>\\end{equation}<br>\\begin{equation}<br>K_{\\rm i} = \\frac{[R][I]}{[RI]}<br>\\end{equation}<br>\\begin{equation}<br>[R_{\\rm T}] = [RI] + [R] + [RL]<br>\\end{equation}<br>\\begin{equation}<br>[R_{\\rm T}] = \\frac{[R][I]}{K_{\\rm i}} + [R] + [RL]<br>\\end{equation}<br>\\begin{equation}<br>[R_{\\rm T}] = \\left(1+\\frac{[I]}{K_{\\rm i}}\\right)[R] + [RL]<br>\\end{equation}<br>\\begin{equation}<br>[R_{\\rm T}] = \\left(1+\\frac{[I]}{K_{\\rm i}}\\right)\\frac{K_{\\rm d}[RL]}{[L]}+ [RL]<br>\\end{equation}<br>\\begin{equation}<br>[RL] = \\frac{[R]_{\\rm T}[L]}{\\left(1+\\frac{[I]}{K_{\\rm i}}\\right)K_{\\rm d} + [L]}<br>\\end{equation}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u8fd1\u4f3c\u3092\u4f7f\u308f\u306a\u3044\u5f0f\u306e\u5c0e\u51fa<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">50%\u7d50\u5408\u963b\u5bb3\u6642<\/h4>\n\n\n\n<p>50%\u7d50\u5408\u963b\u5bb3\u6642\u3092\u8003\u3048\u308b\u3002<\/p>\n\n\n\n<p>\\begin{equation}<br>\\frac{1}{2}[RL]_0 = [RL]_{50}<br>\\end{equation}<br>\\begin{equation}<br>\\frac{1}{2}\\frac{[R]_{\\rm T}[L]_0}{K_{\\rm d} + [L]_0} = \\frac{[R]_{\\rm T}[L]_{50}}{\\left(1+\\frac{[I]_{50}}{K_{\\rm i}}\\right)K_{\\rm d} + [L]_{50}}<br>\\end{equation}<\/p>\n\n\n\n<p>\\begin{equation}<br>2\\frac{K_{\\rm d} }{[L]_0} + 2 = \\left(1+\\frac{[I]_{50}}{K_{\\rm i}}\\right)\\frac{K_{\\rm d} }{[L]_{50}}<br>+ 1<br>\\end{equation}<\/p>\n\n\n\n<p><br>\\begin{equation}<br>2\\frac{[L]_{50}}{[L]_0} + \\frac{[L]_{50}}{K_{\\rm d}} = 1+\\frac{[I]_{50}}{K_{\\rm i}}<br>\\end{equation}<\/p>\n\n\n\n<p><br>\\begin{equation}<br>K_{\\rm i} = \\frac{[I]_{50}}{2\\frac{[L]_{50}}{[L_0]} &#8211; 1 + \\frac{[L]_{50}}{K_{\\rm d}}} \\;\\;\\;\\;\\mbox{(Goldstein and Barrett, 1987)}<br> = \\frac{[I]_{50}}{1 + \\frac{[L]_{50}}{K_{\\rm d}} + 2\\frac{[L]_{50}-[L]_0}{[L]_0}}<br>\\end{equation}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Cheng\u2013Prusoff\u5f0f\u3078\u306e\u5909\u63db<\/h3>\n\n\n\n<p>\u30ec\u30bb\u30d7\u30bf\u30fc\u6fc3\u5ea6 \\([R]\\) \u306b\u5bfe\u3057\u3066 \\([L]\\) \u304c\u5341\u5206\u5927\u304d\u3051\u308c\u3070\u3001\\([L]_0 \\simeq [L]_{50} \\simeq [L]^{*}_{\\rm T}\\)\u306a\u306e\u3067<\/p>\n\n\n\n<p>\\begin{equation}<br>K_{\\rm i} = \\frac{[I]_{50}}{1 + \\frac{[L]^{*}_{\\rm T}}{K_{\\rm d}}}<br>\\end{equation}<\/p>\n\n\n\n<p>\u30ec\u30bb\u30d7\u30bf\u30fc\u6fc3\u5ea6 \\([R]\\) \u306b\u5bfe\u3057\u3066 \\([I]\\) \u304c\u5341\u5206\u5927\u304d\u3051\u308c\u3070\u3001\\([I]_{50}\\) \u306f50%\u963b\u5bb3\u6642\u306e\u30ea\u30ac\u30f3\u30c9\u7dcf\u6fc3\u5ea6\\(\\textrm{IC}_{50}\\)\u3067\u8fd1\u4f3c\u3067\u304d\u308b\u306e\u3067<br>\\begin{equation}<br>K_{\\rm i} = \\frac{\\textrm{IC}_{50}}{1+\\frac{[L]^{*}_{\\rm T}}{K_{\\rm d}}} \\;\\;\\;\\mbox{(Cheng&#8211;Prusoff equation)}<br>\\end{equation}<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u7d50\u5408\u963b\u5bb3\u66f2\u7dda\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3<\/h2>\n\n\n\n<p>\\([RL]_0\\)\u306e\u5024\u306f\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u3092\u89e3\u3044\u3066\u6c42\u3081\u3089\u308c\u308b\uff08\\([R]_{\\mathrm T} = 3.45\\)\u3001\\([L]_{\\mathrm T} = 17\\)\u3001\\(K_{\\mathrm d} = 0.53\\)\u306e\u6642\u3001\\([RL]_0 = 3.321\\)\uff09\u3002<\/p>\n\n\n\n<p>$$ [RL]_0 = \\frac{1}{2}\\left[([R]_{\\rm T} + [L]_{\\rm T} + K_{\\rm d}) &#8211; \\sqrt{([R]_{\\rm T} + [L]_{\\rm T} + K_{\\rm d})^2 &#8211; 4[R]_{\\rm T}[L]_{\\rm T}}\\right] $$<\/p>\n\n\n\n<p>\u540c\u69d8\u306b\u975e\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u5b58\u5728\u4e0b\u3067\u306e \\([RL]\\) \u306f\u904a\u96e2\u578b\u975e\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u6fc3\u5ea6 \\([I]\\) \u3092\u5909\u6570\u3068\u3057\u305f\u4ee5\u4e0b\u306e\u95a2\u6570\u3067\u8868\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<p>$$ [RL] = \\frac{1}{2}\\left\\{\\left[[R]_{\\rm T} + [L]_{\\rm T} + \\left(1+\\frac{[I]}{K_{\\rm i}}\\right)K_{\\rm d}\\right] &#8211; \\sqrt{\\left[[R]_{\\rm T} + [L]_{\\rm T} + \\left(1+\\frac{[I]}{K_{\\rm i}}\\right)K_{\\rm d}\\right]^2 &#8211; 4[R]_{\\rm T}[L]_{\\rm T}}\\right\\} $$<\/p>\n\n\n\n<p>\u904a\u96e2\u578b\u975e\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u6fc3\u5ea6 \\(\\log_{10} [I]\\) \u306b\u5bfe\u3057\u3066\u653e\u5c04\u30ea\u30ac\u30f3\u30c9\u7d50\u5408\u5ea6 \\(\\theta = [RL]\/[RL]_0\\)\u3092\u30d7\u30ed\u30c3\u30c8\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"232\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2019\/03\/inhibitioncurvelabel-300x232.png\" alt=\"\" class=\"wp-image-1620\" srcset=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2019\/03\/inhibitioncurvelabel-300x232.png 300w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2019\/03\/inhibitioncurvelabel-768x593.png 768w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2019\/03\/inhibitioncurvelabel-1024x791.png 1024w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2019\/03\/inhibitioncurvelabel-350x270.png 350w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2019\/03\/inhibitioncurvelabel.png 1340w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><figcaption class=\"wp-element-caption\">\u56f31. \u7d50\u5408\u963b\u5bb3\u66f2\u7dda\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3002 \\([R]_{\\textrm T} = 3.45\\; \\textrm{nM}\\), \\([L]_{\\textrm T} = 17\\; \\textrm{nM}\\), \\(K_{\\textrm d} = 0.53\\; \\textrm{nM}\\), \\(K_{\\textrm i} = 11\\; \\textrm{nM}\\)\u3002\u7e26\u8ef8\u306f\\(\\theta = [RL]\/[RL]_0\\)\u3001\u6a2a\u8ef8\u306f\u904a\u96e2\u578b\u306e\u975e\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u306e\u5bfe\u6570\u6fc3\u5ea6 \\(\\log_{10} [I]\\)\u3002<\/figcaption><\/figure>\n<\/div>\n\n\n<p>\u4e0a\u306e\u56f31\u306e\u6a2a\u8ef8\u3092unlabelled ligand\u306e\u5bfe\u6570\u6fc3\u5ea6 \\(\\log_{10} [I]_{\\textrm T}\\) \u306b\u5909\u66f4\u3057\u305f\u3002\u306a\u304a\u3001<\/p>\n\n\n\n<p>$$ [I]_{\\mathrm T} = [I] + [RI] $$<\/p>\n\n\n\n<p>$$ [RI] = [R]_{\\mathrm{T}} &#8211; \\frac{[L]_0}{[L]_{\\mathrm T} &#8211; [RL]}\\frac{[RL]}{[RL]_0}[R]_{\\mathrm{T}} + \\left( \\frac{[L]_0}{[L]_{\\mathrm T} &#8211; [RL]} &#8211; 1\\right) [RL] \\;\\; .$$<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"237\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/7278bb4d995a5cc1236d2fed58a07f8e-300x237.png\" alt=\"\" class=\"wp-image-3043\" srcset=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/7278bb4d995a5cc1236d2fed58a07f8e-300x237.png 300w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/7278bb4d995a5cc1236d2fed58a07f8e-768x606.png 768w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/7278bb4d995a5cc1236d2fed58a07f8e.png 936w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><figcaption class=\"wp-element-caption\">\u56f32. \u7d50\u5408\u963b\u5bb3\u66f2\u7dda\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3. \u6a2a\u8ef8\u304c\u5168\u975e\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u306e\u5bfe\u6570\u6fc3\u5ea6 \\(\\log_{10} [I]_{\\textrm T}\\).<\/figcaption><\/figure>\n<\/div>\n\n\n<p>data.csv<\/p>\n\n\n\n<pre class=\"prettyprint\">logIT,theta\n-9.495,0.999\n-8.995,0.997\n-8.495,0.990\n-7.995,0.968\n-7.496,0.906\n-6.996,0.759\n-6.498,0.512\n-5.999,0.259\n-5.500,0.102\n-5.000,0.035\n-4.500,0.011\n-4.000,0.004<\/pre>\n\n\n\n<h2 class=\"wp-block-heading\">\u975e\u7dda\u5f62\u56de\u5e30\u306b\u3088\u308b<em>K<\/em><sub>i<\/sub>\u306e\u63a8\u5b9a<\/h2>\n\n\n\n<p><a href=\"https:\/\/www.r-project.org\/\" title=\"\">\u7d71\u8a08\u89e3\u6790\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2R<\/a>\u3092\u4f7f\u3063\u3066\u975e\u7dda\u5f62\u56de\u5e30\u3092\u884c\u3046\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">[<em>I<\/em>] \u306e\u95a2\u6570\u3078\u306e\u975e\u7dda\u5f62\u56de\u5e30<\/h3>\n\n\n\n<p>$$ \\theta  = \\frac{1}{[RL]_0} \\times \\frac{1}{2}\\left\\{\\left[[R]_{\\rm T} + [L]_{\\rm T} + \\left(1+\\frac{[I]}{K_{\\rm i}}\\right)K_{\\rm d}\\right] &#8211; \\sqrt{\\left[[R]_{\\rm T} + [L]_{\\rm T} + \\left(1+\\frac{[I]}{K_{\\rm i}}\\right)K_{\\rm d}\\right]^2 &#8211; 4[R]_{\\rm T}[L]_{\\rm T}}\\right\\} $$<\/p>\n\n\n\n<p>\\([I]\\) \u306e\u5909\u308f\u308a\u306b \\([I]_\\mathrm{T} (= [I] + [RI]) \\) \u3092\u4f7f\u3044\u305f\u3044\u304c\u3001\\([RI]\\) \u306e\u5f0f\u306b \\([RL]\\) \u304c\u542b\u307e\u308c\u3066\u3057\u307e\u3046\u3002\u3053\u3053\u3067\u306f\u3001\\([I] \\simeq [I]_\\mathrm{T} &#8211; [R]_\\mathrm{T}\/2) \\) \u3068\u3044\u3046\u7c21\u5358\u306a\u88dc\u6b63\u3092\u4f7f\u7528\u3057\u3066\u3001\u7f6e\u63db\u3059\u308b\u3002\u3059\u308b\u3068 \\([I]_\\mathrm{T}\\) \u306e\u95a2\u6570<\/p>\n\n\n\n<p>$$ \\theta = \\frac{1}{[RL]_0} \\times \\frac{1}{2}\\left\\{\\left[[R]_{\\rm T} + [L]_{\\rm T} + \\left(1+\\frac{[I]_\\mathrm{T} &#8211; [R]_\\mathrm{T}\/2}{K_{\\rm i}}\\right)K_{\\rm d}\\right] &#8211; \\sqrt{\\left[[R]_{\\rm T} + [L]_{\\rm T} + \\left(1+\\frac{[I]_\\mathrm{T} &#8211; [R]_\\mathrm{T}\/2}{K_{\\rm i}}\\right)K_{\\rm d}\\right]^2 &#8211; 4[R]_{\\rm T}[L]_{\\rm T}}\\right\\} $$<\/p>\n\n\n\n<p>\u304c\u5f97\u3089\u308c\u308b\u3002\u4e0a\u5f0f\u306b\u304a\u3044\u3066 (\\( [R]_{\\rm T} = 3.45; [L]_{\\rm T} = 17; K_{\\rm d} = 0.53; [RL]_0 = 3.3213\\)\uff08\u5358\u4f4d\u306fnM\uff09\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<pre class=\"prettyprint\">simulation &lt;- read.csv(&#34;data.csv&#34;)\nsimulation$IT &lt;- 10^(simulation$logIT + 9)\nresult1 &lt;- nls(\n   theta ~ 1&#47;3.3213 * 1&#47;2 * ((3.45 + 17 + (1+ (IT - 3.45&#47;2)&#47;Ki)*0.53) - sqrt((3.45 + 17 + (1+ (IT - 3.45&#47;2)&#47;Ki)*0.53)^2 - 4*3.45*17)),\n   data = simulation,\n   start = c(Ki = 20)\n )\nsummary(result1)\n<\/pre>\n\n<p><b>Output<\/b>:<\/p>\n<pre class=\"prettyprint\">\nFormula: theta ~ 1&#47;3.3213 * 1&#47;2 * ((3.45 + 17 + (1 + (IT - 3.45&#47;2)&#47;Ki) * \n    0.53) - sqrt((3.45 + 17 + (1 + (IT - 3.45&#47;2)&#47;Ki) * 0.53)^2 - \n    4 * 3.45 * 17))\n\nParameters:\n   Estimate Std. Error t value Pr(&gt;|t|)    \nKi 10.96500    0.09913   110.6   &lt;2e-16 ***\n---\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n\nResidual standard error: 0.003358 on 11 degrees of freedom\n\nNumber of iterations to convergence: 5 \nAchieved convergence tolerance: 1.366e-06\n<\/pre>\n\n\n\n<p>\u5f97\u3089\u308c\u305f<em>K<\/em><sub>i<\/sub>\u5024\u306f10.965 nM\u3060\u3063\u305f\uff08\u6b63\u89e3\u306f11 nM\uff09\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u56de\u5e30\u306b\u3088\u308bIC<sub>50<\/sub>\u306e\u63a8\u5b9a<\/h2>\n\n\n\n<p>\u5b9f\u9a13\u7684\u306b\u306f\u7d50\u5408\u963b\u5bb3\u66f2\u7dda\u306e\u88fe\u306e\u65b9\u306f\u4fe1\u983c\u6027\u304c\u4f4e\u3044\u306e\u3067\u3001\u50be\u304d\u304c\u5927\u304d\u306a\u7d50\u5408\u5ea650%\u4ed8\u8fd1\u306e\u30c7\u30fc\u30bf\u70b9\u304b\u3089IC<sub>50<\/sub>\u3092\u63a8\u5b9a\u3057\u3066\u3001IC<sub>50<\/sub>\u3092<em>K<\/em><sub>i<\/sub>\u306b\u5909\u63db\u3057\u305f\u3044\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u30b7\u30b0\u30e2\u30a4\u30c9\u3078\u306e\u975e\u7dda\u5f62\u56de\u5e30<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-left\"><strong>\u76f8\u88dc\u8aa4\u5dee\u95a2\u6570\uff08erfc\uff09<\/strong>\u306b\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0<\/h4>\n\n\n\n<p>$${\\rm erfc}(x) = \\frac{2}{\\sqrt{\\pi}}\\int_{x}^{\\infty}e^{-t^{2}}\\,dt$$<\/p>\n\n\n\n<p>\uff08\u7814\u7a76\u5ba4\u306b\u5165\u3063\u305f\u3053\u308d\u306fR\u3084Excel\u3092\u4f7f\u308f\u305a\u306b\u3001<a href=\"https:\/\/www.ars.usda.gov\/pacific-west-area\/parlier\/sjvasc\/cpq\/docs\/priprobit-download\" title=\"\">PriProbit<\/a>\u30d7\u30ed\u30b0\u30e9\u30e0 (<a href=\"https:\/\/doi.org\/10.1303\/aez.33.339\" title=\"\">Sakuma, 1998<\/a>) \u3092\u4f7f\u3063\u3066IC<sub>50<\/sub>\u3092\u6c42\u3081\u3066\u3044\u307e\u3057\u305f\u3002\uff09<\/p>\n\n\n\n<p>Probit\u95a2\u6570\u306f\u6b63\u898f\u5206\u5e03\u306e\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\\(\\Phi\\)\u306e\u9006\u95a2\u6570\u3067\u3042\u308b\u3002\u76f8\u88dc\u8aa4\u5dee\u95a2\u6570 erfc \u3068\\(\\Phi\\)\u306b\u306f\u6b21\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3064: \\(\\Phi (x) = \\frac{1}{2} {\\rm erfc}\\left(-\\frac{x}{\\sqrt{2}}\\right)\\)\u3002<\/p>\n\n\n\n<pre class=\"prettyprint\">simulation &lt;- read.csv(&#34;data.csv&#34;)\nerfc &lt;- function(x) 2 * pnorm(x * sqrt(2), lower=FALSE) \nresult2 = nls(theta~1&#47;2*erfc((logIT - logIC50)&#47;a), data = simulation, start = c(logIC50=-6.5, a=1))\nsummary(result2)\n<\/pre>\n<p><b>Formula<\/b>: $$\\theta = \\frac{1}{2}\\cdot\\mbox{erfc}\\left(\\frac{\\log[I]_{\\rm T} - \\log{\\rm IC}_{50}}{a}\\right)$$<\/p>\n\n<p>\uff08\u203b\u7bc4\u56f2\u30920\u304b\u30891\u306b\u3059\u308b\u305f\u30811\/2\u3092\u639b\u3051\u3066\u3044\u308b\uff09<\/p>\n<p><b>Output<\/b>:<\/p>\n<pre class=\"prettyprint\">\nFormula: theta ~ 1&#47;2 * erfc((logIT - logIC50)&#47;a)\n\nParameters:\n         Estimate Std. Error t value Pr(&gt;|t|)    \nlogIC50 -6.476263   0.006851 -945.27  &lt; 2e-16 ***\na        1.082295   0.013710   78.94  2.6e-15 ***\n---\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n\nResidual standard error: 0.005889 on 10 degrees of freedom\n\nNumber of iterations to convergence: 5 \nAchieved convergence tolerance: 6.534e-07\n<\/pre>\n\n\n\n<p>\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u5ea6\u5408\u3044\u306e\u53ef\u8996\u5316<\/p>\n\n\n\n<pre class=\"prettyprint\">concpre = seq(-10,-3.5, length=100)\nplot(theta~logIT,data=simulation,xlim=c(-10,-3.5),ylim=c(0,1))\nlines(concpre, predict(result2, newdata=list(logIT=concpre)))\n<\/pre>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"300\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Rplot_erfc-300x300.png\" alt=\"\" class=\"wp-image-3045\" srcset=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Rplot_erfc-300x300.png 300w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Rplot_erfc-1024x1024.png 1024w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Rplot_erfc-150x150.png 150w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Rplot_erfc-768x768.png 768w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Rplot_erfc-1536x1536.png 1536w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Rplot_erfc-2048x2048.png 2048w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n<\/div>\n\n\n<p>\u30ab\u30fc\u30d6\u306e\u90e8\u5206\u3067\u3042\u307e\u308a\u5f53\u3066\u5d4c\u307e\u308a\u304c\u826f\u304f\u306a\u3044\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u6e1b\u5c11\u3059\u308b<strong>\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u95a2\u6570 \\(1\/(1 + \\exp(ax))\\)<\/strong> \u306b\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0<\/h4>\n\n\n\n<p>\u6a19\u6e96\u30b7\u30b0\u30e2\u30a4\u30c9\u95a2\u6570\u306f$$f(x) = \\frac{1}{1 + e^{-ax}}\\;\\;\\mbox{\u3002}$$<\/p>\n\n\n\n<p>\u6e1b\u5c11\u3059\u308b\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u95a2\u6570\u306f1 \u2212 \u6a19\u6e96\u30b7\u30b0\u30e2\u30a4\u30c9\u95a2\u6570: $$f(x) = 1 - \\frac{1}{1 + e^{-ax}} = \\frac{1}{1 + e^{ax}}\\;\\;\\mbox{\u3002}$$<\/p>\n\n\n\n<pre class=\"prettyprint\">result3 = nls(theta~1&#47;(1+exp(a*log(10)*(logIT - logIC50))), data = simulation, start = c(logIC50=-6.5, a=1))\nsummary(result3)\n<\/pre>\n<p><b>Formula<\/b>: $$\\theta = \\frac{1}{1 + e^{a \\log_{e} 10 (\\log_{10}[I]_{\\rm T} - \\log_{10}{\\rm IC}_{50})}}$$<\/p>\n<p><b>Output<\/b>:<\/p>\n<pre class=\"prettyprint\">Formula: theta ~ 1&#47;(1 + exp(a * log(10) * (logIT - logIC50)))\n\nParameters:\n         Estimate Std. Error t value Pr(&gt;|t|)    \nlogIC50 -6.476238   0.001243 -5209.7   &lt;2e-16 ***\na        0.964276   0.002346   411.1   &lt;2e-16 ***\n---\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n\nResidual standard error: 0.001071 on 10 degrees of freedom\n\nNumber of iterations to convergence: 4 \nAchieved convergence tolerance: 8.128e-08\n<\/pre>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"300\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Rplot_sigmoid-300x300.png\" alt=\"\" class=\"wp-image-3046\" srcset=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Rplot_sigmoid-300x300.png 300w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Rplot_sigmoid-1024x1024.png 1024w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Rplot_sigmoid-150x150.png 150w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Rplot_sigmoid-768x768.png 768w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Rplot_sigmoid-1536x1536.png 1536w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Rplot_sigmoid-2048x2048.png 2048w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n<\/div>\n\n\n<p>\u6e1b\u5c11\u3059\u308b\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u95a2\u6570\u306b\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u30c7\u30fc\u30bf\u306f\u5b8c\u74a7\u306b\u5f53\u3066\u5d4c\u307e\u3063\u3066\u3044\u308b\u3088\u3046\u306b\u898b\u3048\u308b\u3002log<sub>10<\/sub> IC<sub>50<\/sub> = -6.476238\u3001<em>a<\/em> = 0.964276\u3060\u3063\u305f\u3002\u3053\u306e\u66f2\u7dda\u306f\u751f\u7269\u5b66\u30fb\u85ac\u7406\u5b66\u5206\u91ce\u3067\u300c<strong>\u963b\u5bb3\u66f2\u7dda<\/strong>\u300d\u3068\u547c\u3070\u308c\u308b\u3002\u30d1\u30e9\u30e1\u30fc\u30bf<em>a<\/em>\u306f\u30b7\u30b0\u30e2\u30a4\u30c9\u66f2\u7dda\u306e\u50be\u304d\u3092\u8a18\u8ff0\u3059\u308b\u30ea\u30ac\u30f3\u30c9\u306e<a href=\"https:\/\/en.wikipedia.org\/wiki\/Hill_equation_(biochemistry)#Hill_coefficient\" title=\"\">\u30d2\u30eb\u4fc2\u6570 <em>n<\/em><sub><em>H<\/em><\/sub><\/a>\u3067\u3042\u308b\u3002\u4ee5\u4e0b\u306b\u5909\u63db\u3092\u793a\u3059\u3002<\/p>\n\n\n\n<p>\u307e\u305a\u30012\u3064\u4e0b\u306e\u7bc0\u306b\u793a\u3059\u3088\u3046\u306b<em>\u03b8<\/em>\u306f<\/p>\n\n\n\n<p>$$\\theta = \\frac{\\frac{[L]}{[L]_0} (K_{\\rm d} + [L]_0)}{\\frac{K_{\\rm d}}{K_{\\rm i}}[I] + K_{\\rm d} + [L]} $$<\/p>\n\n\n\n<p>\u3068\u8868\u308f\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002\\([L] \\simeq [L]_0\\)\u3001\\([I] \\simeq [I]_{\\mathrm T}\\)\u306a\u3089\u3070<\/p>\n\n\n\n<p>$$\\theta = \\frac{1}{1 + \\frac{1}{K_{\\rm d} + [L]_0}\\frac{K_{\\rm d}}{K_{\\rm i}} [I]_{\\mathrm T}} $$<\/p>\n\n\n\n<p>$$\\theta = \\frac{1}{1 + \\exp\\left\\{\\log_{e} 10 \\left[\\log_{10} [I]_{\\mathrm T} - \\log_{10} K_{\\mathrm i}\\left( 1+ \\frac{[L]_0}{K_\\mathrm{d}} \\right) \\right]\\right\\}} $$<\/p>\n\n\n\n<p>\u3068\u66f8\u3051\u308b\u3002Cheng\u2013Prusoff\u5f0f\u304b\u3089\\(  K_{\\mathrm i}\\left( 1+ \\frac{[L]_0}{K_\\mathrm{d}}  \\right) \\simeq \\mathrm{IC}_{50} \\) \u306a\u306e\u3067\u3001<\/p>\n\n\n\n<p>$$\\theta = \\frac{1}{1 + \\exp\\left[\\log_{e} 10 \\left(\\log_{10} [I]_{\\mathrm T} - \\log_{10} \\mathrm{IC}_{50} \\right)\\right]} $$<\/p>\n\n\n\n<p>\u3068\u8fd1\u4f3c\u7684\u306b\u8868\u308f\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<p>\u5b9f\u969b\u4e0a\u306f\u76f8\u88dc\u8aa4\u5dee\u95a2\u6570\u3092\u4f7f\u3063\u3066\u3082\u307b\u3068\u3093\u3069\u540c\u3058IC<sub>50<\/sub>\u304c\u5f97\u3089\u308c\u3066\u3044\u308b\u304c\u3001\u30e2\u30c7\u30eb\u3068\u3057\u3066\u306f\u3053\u3061\u3089\u306e\u65b9\u304c\u512a\u308c\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7dda\u5f62\u56de\u5e30<\/h3>\n\n\n\n<p>\u6b21\u306b\u7dda\u5f62\u56de\u5e30\u3092\u9069\u7528\u3059\u308b\u305f\u3081\uff08Microsoft Excel\u304c\u4f7f\u3048\u308b!\uff09\u306e\u7dda\u5f62\u30b0\u30e9\u30d5\u3078\u306e\u5909\u63db\u3092\u793a\u3059\u3002<\/p>\n\n\n\n<p>\u975e\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u306e\u5bfe\u6570\u6fc3\u5ea6\u306b\u5bfe\u3057\u3066 \\(\\log_{10} \\{\\theta\/(1- \\theta)\\}\\) \u3092\u30d7\u30ed\u30c3\u30c8\u3059\u308b\u3068\uff08<strong>\u30d2\u30eb\u30d7\u30ed\u30c3\u30c8<\/strong>\uff09\u3001\u50be\u304d\u304c\u22121\u306b\u8fd1\u3044\u7dda\u5f62\u30b0\u30e9\u30d5\u304c\u5f97\u3089\u308c\u308b\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"959\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/logI_linear-1024x959.png\" alt=\"\" class=\"wp-image-6658\" style=\"aspect-ratio:1.067789540588317;width:355px;height:auto\" srcset=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/logI_linear-1024x959.png 1024w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/logI_linear-300x281.png 300w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/logI_linear-768x719.png 768w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/logI_linear-1536x1439.png 1536w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/logI_linear-2048x1918.png 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">\u56f33. logistic\u95a2\u6570 (\\(\\log_{10} \\frac{p}{1 - p}\\)) \u3067fitting\u3002\u7e26\u8ef8\u306f\\(\\log_{10} \\frac{\\theta}{1 - \\theta}\\)\u3001\u6a2a\u8ef8\u306ffree\u306eunlabelled ligand\u306e\u6fc3\u5ea6 \\([I]\\)\u3002\u7dcf\u30ec\u30bb\u30d7\u30bf\u30fc\u6fc3\u5ea6 \\([R]_{\\textrm T}\\) \u304c\u5c0f\u3055\u304f\u306a\u308b\u7a0b\u3001\u50be\u304d\u304c\u22121\u306b\u8fd1\u3065\u304f\u3002<\/figcaption><\/figure>\n<\/div>\n\n\n<p>\u6a2a\u8ef8\u3092\u52a0\u3048\u305f\u30ea\u30ac\u30f3\u30c9\u306e\u7dcf\u6fc3\u5ea6log<sub>10<\/sub>[<em>I<\/em>]<sub>T<\/sub> \u306b\u5909\u3048\u3066\u30d7\u30ed\u30c3\u30c8\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"959\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/logIT_linear-1024x959.png\" alt=\"\" class=\"wp-image-6659\" style=\"aspect-ratio:1.067789540588317;width:327px;height:auto\" srcset=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/logIT_linear-1024x959.png 1024w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/logIT_linear-300x281.png 300w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/logIT_linear-768x719.png 768w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/logIT_linear-1536x1439.png 1536w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/logIT_linear-2048x1918.png 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p>\u305d\u3057\u3066\u3001Microsoft Excel\u306eSLOPE\u95a2\u6570\u3068INTERCEPT\u95a2\u6570\u3092\u4f7f\u3063\u3066\u8a08\u7b97\u3057\u305flog IC<sub>50<\/sub>\u306f\u22126.4765\u3068\u306a\u308a\u3001\u975e\u7dda\u5f62\u56de\u5e30\uff08\u30b7\u30b0\u30e2\u30a4\u30c9\u95a2\u6570\uff09\u304b\u3089\u6c42\u3081\u305flog IC<sub>50<\/sub>\uff08-6.4762\uff09\u3068\u6709\u52b9\u6570\u5b574\u6841\u307e\u3067\u4e00\u81f4\u3059\u308b\uff08nM\u5358\u4f4d\u306b\u5909\u63db\u3059\u308b\u3068\u305d\u308c\u305e\u308c333.8 nM\u304a\u3088\u3073334.0 nM\uff09\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u306a\u305c \\(\\log \\{\\theta\/(1 \u2013 \\theta)\\}\\) \u3092 \\(\\log [I]\\) \u306b\u5bfe\u3057\u3066\u30d7\u30ed\u30c3\u30c8\u3059\u308b\u3068\u50be\u304d \\(-1\\) \u306e\u76f4\u7dda\u306b\u306a\u308b\u306e\u304b<\/h3>\n\n\n\n[<em>RL<\/em>]<sub>0<\/sub> \u3068[<em>RL<\/em>] \u3092\u524d\u7bc0\u306e\u3088\u3046\u306a\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u3068\u3057\u3066\u3067\u306f\u306a\u304f\u3001<\/p>\n\n\n\n<p>$$ [RL]_0 = \\frac{[R]_{\\rm T}[L]_0}{K_{\\rm d} + [L]_0} $$<\/p>\n\n\n\n<p>$$ [RL] = \\frac{[R]_{\\rm T}[L]}{\\left(1+\\frac{[I]}{K_{\\rm i}}\\right)K_{\\rm d} + [L]} $$<\/p>\n\n\n\n<p>\u3068\u8868\u3059\u3068\u3001\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u7d50\u5408\u5ea6 <em>\u03b8<\/em> = [<em>RL<\/em>]\/[<em>RL<\/em>]<sub>0<\/sub> \u306f\u3001<\/p>\n\n\n\n<p> $$\\theta = \\frac{[R]_{\\rm T}[L]}{\\left(1+\\frac{[I]}{K_{\\rm i}}\\right)K_{\\rm d} + [L]} \\times \\frac{K_{\\rm d} + [L]_0}{[R]_{\\rm T}[L]_0}$$ $$\\theta = \\frac{\\frac{[L]}{[L]_0} (K_{\\rm d} + [L]_0)}{\\frac{K_{\\rm d}}{K_{\\rm i}}[I] + K_{\\rm d} + [L]} $$<\/p>\n\n\n\n<p>\u3068\u8868\u308f\u3055\u308c\u308b\u306e\u3067\uff0c<\/p>\n\n\n\n<p>\\begin{equation}<br>\\frac{\\theta}{1-\\theta} = \\frac{\\frac{[L]}{[L]_0}(K_{\\rm d} + [L]_0)}{\\frac{K_{\\rm d}}{K_{\\rm i}}[I] + K_{\\rm d} + [L] - \\frac{[L]}{[L]_0}(K_{\\rm d} + [L]_0)} =  \\frac{\\frac{[L]}{[L]_0} K_{\\rm d} + [L]}{\\frac{K_{\\rm d}}{K_{\\rm i}}[I] + \\left(1 - \\frac{[L]}{[L]_0}\\right) K_{\\rm d}}<br>\\end{equation}<\/p>\n\n\n\n<p>\u3068\u3044\u3046\u95a2\u4fc2\u5f0f\u304c\u5f97\u3089\u308c\u308b\u3002<\/p>\n\n\n\n<p>\\([L]_0 \\simeq [L]\\)\u304c\u6210\u308a\u7acb\u3064\u3068\u3059\u308b\u3068\u3001<\/p>\n\n\n\n<p>\\begin{equation}<br>\\frac{\\theta}{1-\\theta} = \\frac{K_{\\rm d} + [L]}{\\frac{K_{\\rm d}}{K_{\\rm i}}[I]}<br>\\end{equation}<\/p>\n\n\n\n<p>\u3068\u5f0f\u306f\u7c21\u5358\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<p>\u4e21\u8fba\u306e\u5bfe\u6570\u3092\u53d6\u308b\uff08\u3053\u3053\u3067\u306f\u5e38\u7528\u5bfe\u6570\uff09\u3068\u3001free\u306e\u30ea\u30ac\u30f3\u30c9\u5bfe\u6570\u6fc3\u5ea6 \\(\\log<sub>10<\/sub>[I]\\) \u306b\u5bfe\u3057\u3066\u50be\u304d\\(-1\\)\u306e\u76f4\u7dda\u95a2\u4fc2\u306b\u306a\u308b\u3002<br>\\begin{equation}<br>\\log_{10} \\left(\\frac{\\theta}{1-\\theta}\\right) = -\\log_{10} [I] -\\log_{10} K_{\\rm d} + \\log_{10} K_{\\rm i} + \\log_{10} (K_{\\rm d} + [L]) \\simeq -\\log_{10} [I]  + \\log_{10} \\mathrm{IC}_{50}<br>\\end{equation}<\/p>\n\n\n\n<p>\u4e0a\u5f0f\u306b\u304a\u3044\u3066 [<em>L<\/em>] \u306f\u5909\u6570 [<em>I<\/em>] \u306b\u4f9d\u5b58\u3059\u308b\u3002<\/p>\n\n\n\n<p>\u30ed\u30b8\u30c3\u30c8\u95a2\u6570\uff08\\(\\log \\{p\/(1-p)\\}\\)\uff09\u3068\u30b7\u30b0\u30e2\u30a4\u30c9\u95a2\u6570\u306f\u9006\u95a2\u6570\u306e\u95a2\u4fc2\u306b\u3042\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7d50\u5408\u5ea6\u03b8\u304b\u3089<em>K<\/em><sub>i<\/sub>\u5024\u3078\u306e\u7c21\u6613\u306a\u5909\u63db<\/h3>\n\n\n\n<p>\u7d50\u5408\u963b\u5bb3\u304c50%\u3092\u5207\u3089\u306a\u3044\u7a0b\u5f31\u3044\u30ea\u30ac\u30f3\u30c9\u306b\u3064\u3044\u3066\u30011\u70b9\u304b\u3089\\(K_{\\rm i}\\)\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3068\u3057\u3066<br>\\begin{equation}<br>\\frac{\\theta}{1-\\theta} = \\frac{K_{\\rm d} + [L]}{\\frac{K_{\\rm d}}{K_{\\rm i}}[I]}<br>\\end{equation}<br>\u3092\u5909\u5f62\u3059\u308b\u3068\u3001<br>\\begin{equation}<br>K_{\\rm i} = \\left(\\frac{\\theta}{1-\\theta}\\right) \\frac{K_{\\rm d}[I]}{K_{\\rm d} + [L]}<br>\\end{equation}<br>\u30ec\u30bb\u30d7\u30bf\u30fc\u6fc3\u5ea6 \\([R]\\) \u306b\u5bfe\u3057\u3066 \\([I]\\) \u304c\u5341\u5206\u5927\u304d\u3051\u308c\u3070\uff08\u5f31\u3044\u30ea\u30ac\u30f3\u30c9\u306a\u306e\u3067\u3053\u308c\u3092\u6e80\u305f\u3059\uff09\u3001 \\([I]\\) \u306f\u30ea\u30ac\u30f3\u30c9\u7dcf\u6fc3\u5ea6 \\([I]_{\\textrm T}\\) \u3067\u8fd1\u4f3c\u3067\u304d\u308b\u306e\u3067<br>\\begin{equation}<br>K_{\\rm i} = \\left(\\frac{\\theta}{1-\\theta}\\right) \\frac{K_{\\rm d}[I]_{\\rm T}}{K_{\\rm d} + [L]}<br>\\end{equation}<\/p>\n\n\n\n<p>\u53b3\u5bc6\u306a\u5909\u63db\u306b\u306f\u5f8c\u8ff0\u306eDandliker\u306e\u5f0f\u3092\u4f7f\u7528\u3059\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u975e\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u306e\u7d50\u5408\u80fd\u304c\u9ad8\u3044\uff08Tight-binding ligand\uff09\u306e\u5834\u5408<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">IC50\u306b\u5bfe\u3059\u308b\u88dc\u6b63<\/h3>\n\n\n\n<p>\u30ec\u30bb\u30d7\u30bf\u30fc\u6fc3\u5ea6 \\([R]\\) \u306b\u5bfe\u3057\u3066 \\([I]\\) \u304c\u5341\u5206\u5927\u304d\u304f\u306a\u3044\u5834\u5408 (\u975e\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u306e\u7d50\u5408\u80fd\u304c\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9 [<sup>3<\/sup>H]PDBu\u306e\u7d50\u5408\u3068\u540c\u7b49\u3042\u308b\u3044\u306f\u305d\u308c\u4ee5\u4e0a\u306e\u5834\u5408)\u3001\\([I]\\) \u3092\u30ea\u30ac\u30f3\u30c9\u7dcf\u6fc3\u5ea6 \\([I]_{\\rm T}\\) \u3067\u8fd1\u4f3c\u3067\u304d\u306a\u3044\u3002\u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n<p>$$ [I]_{50} = \\mathrm{IC}_{50} - [RI]_{50} $$<\/p>\n\n\n\n<p>\u306e \\([RI]_{50} \\)\u3092\u8a08\u7b97\u3057\u305f\u3044\u3002<\/p>\n\n\n\n<p>\u5b9f\u9a13\u7684\u306b\u306f\u653e\u5c04\u6d3b\u6027\u304b\u3089 \\([RL]_0\\)\u3001\\([L]_{0}\\)\u3092\u6e2c\u5b9a\u3067\u304d\u3001\u305d\u308c\u3089\u306e\u5024\u3068\u65e2\u77e5\u306e<em>K<\/em><sub>d<\/sub>\u5024\u304b\u3089 \\([L]_{50} = [L]_{0} + [RL]_{0}\/2\\)\u3001\\([R]_{\\mathrm{T}} = [RL]_0 (1 + K_{\\mathrm d}\/[L]_0)\\)\u3001\\([RL]_{50} = [RL]_{0}\/2\\)\u3092\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p>\u307e\u305a\u3001\u4ee5\u4e0b\u306e2\u3064\u306e\u4fdd\u5b58\u5f0f\u3092\u8003\u3048\u308b\u3002<\/p>\n\n\n\n<p>I\u304c\u5b58\u5728\u3057\u306a\u3044\u6642: $$ [R]_{\\mathrm{T}} = [R]_{0} + [RL]_{0} $$<\/p>\n\n\n\n<p>I\u306e\u6fc3\u5ea6\u304c \\([I]_{50}\\)\u306e\u6642: $$ [R]_{\\mathrm{T}} = [R]_{50} + [RL]_{50} + [RI]_{50} $$<\/p>\n\n\n\n<p>\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9L\u306e\u5e73\u8861\u3092\u8003\u3048\u308b\u3068<\/p>\n\n\n\n<p>$$K_{\\mathrm d} = \\frac{[R]_0[L]_0}{[RL]_0} = \\frac{[R]_{50}[L]_{50}}{[RL]_{50}} $$<\/p>\n\n\n\n<p>\u304c\u6210\u308a\u7acb\u3063\u3066\u3044\u308b\u3002\u3053\u306e\u5f0f\u306b \\( [R]_{0} =  [R]_{\\mathrm{T}} - [RL]_{0}\\)\u304a\u3088\u3073\\( [R]_{50} =  [R]_{\\mathrm{T}} - [RL]_{50} - [RI]_{50}\\)\u3092\u4ee3\u5165\u3057\u3066\u5909\u5f62\u3059\u308b\u3068\u3001<\/p>\n\n\n\n<p>$$ [RI]_{50} = [R]_{\\mathrm{T}} - \\frac{[L]_0}{[L]_{50}}\\frac{[RL]_{50}}{[RL]_0}[R]_{\\mathrm{T}} + \\left( \\frac{[L]_0}{[L]_{50}} - 1\\right) [RL]_{50} $$<\/p>\n\n\n\n<p>\u3068\u306a\u308b\u3002\\(\\frac{[RL]_{50}}{[RL]_0} = 1\/2\\) \u306a\u306e\u3067\u3001<\/p>\n\n\n\n<p>$$ [RI]_{50} = \\left( 1 - \\frac{1}{2} \\frac{[L]_0}{[L]_{50}} \\right)[R]_{\\mathrm{T}} +  \\left( \\frac{[L]_0}{[L]_{50}} - 1\\right) [RL]_{50} $$<\/p>\n\n\n\n<p>\u3068\u306a\u308b\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u88dc\u6b63\u5f0f<\/p>\n\n\n\n<p>$$ K_{\\rm i} = \\frac{\\mathrm{IC}_{50} - \\left( 1 - \\frac{1}{2} \\frac{[L]_0}{[L]_{50}} \\right)[R]_{\\mathrm{T}} - \\left( \\frac{[L]_0}{[L]_{50}} - 1\\right) \\frac{[RL]_{0}}{2} }{2\\frac{[L]_{50}}{[L]_0} - 1 + \\frac{[L]_{50}}{K_{\\rm d}}} $$<\/p>\n\n\n\n<p>\u304c\u5c0e\u304b\u308c\u308b\u3002<strong>\u3053\u306e\u88dc\u6b63\u5f0f\u304b\u3089\u5f97\u3089\u308c\u308b<em>K<\/em><sub>i<\/sub>\u5024\u306f\u53b3\u5bc6\u306a\u5024\u3067\u3042\u308a\u3001\u6b21\u7bc0\u306eMunson\u2013Rodbard\u88dc\u6b63\u3068\u7b49\u4fa1\u3067\u3042\u308b\u3002<\/strong><\/p>\n\n\n\n<p>\u3082\u3057\u3001\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u6fc3\u5ea6\u304c\u30ec\u30bb\u30d7\u30bf\u30fc\u6fc3\u5ea6\u306b\u5bfe\u3057\u3066\u5341\u5206\u904e\u5270\u3067\\( [L]_0 \\approx [L]_{50}\\) \u3068\u3044\u3046\u8fd1\u4f3c\u3092\u4f7f\u3048\u308b\u3068\u3059\u308b\u3068\u3001\u4e0a\u5f0f\u306e\u53f3\u8fba\u306e\u5206\u5b50\u306f\u3088\u308a\u5358\u7d14\u306b\u306a\u308a\u3001<\/p>\n\n\n\n<p>$$ K_{\\rm i} = \\frac{\\mathrm{IC}_{50} - \\frac{[R]_{\\mathrm{T}}}{2}} {2\\frac{[L]_{50}}{[L]_0} - 1 + \\frac{[L]_{50}}{K_{\\rm d}}} $$<\/p>\n\n\n\n<p>\u3068\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u3002<strong>\u5b9f\u969b\u4e0a\u306f\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u6fc3\u5ea6\u304c\u5341\u5206\u904e\u5270\u3067\u306a\u3044\u5834\u5408\u3067\u3082\u3001\u3053\u306e\u7c21\u5358\u306a\u88dc\u6b63\u3067\u5f97\u3089\u308c\u308b<em>K<\/em><sub>i<\/sub>\u3067\u7cbe\u5ea6\u7684\u306b\u5168\u304f\u554f\u984c\u306a\u3044\u3002<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span style=\"font-weight: bold;\">Munson\u2013Rodbard<\/span>\u88dc\u6b63<\/h3>\n\n\n\n<p>Munson\u2013Rodbard\u5f0f\u304b\u3089IC<sub>50<\/sub>\uff08\u7dcf\u6fc3\u5ea6\uff09\u3092\u4f7f\u7528\u3057\u3066\uff08\\([I]_{50} \\simeq \\textrm{IC}_{50}\\) \u306e\u8fd1\u4f3c\u3092\u4f7f\u308f\u305a\u306b\uff09\\(K_{\\textrm i}\\) \u3092\u53b3\u5bc6\u306b\u7b97\u51fa\u3067\u304d\u308b (Munson ad Rodbard, 1988; Huang, 2003)\u3002<\/p>\n\n\n\n<p>\\(y_0 = [RL]_0\/[L]_0\\) \u3068\u3059\u308b\u3068\u3001<\/p>\n\n\n\n<p>\\begin{equation}<br>K_{\\rm i} = \\frac{\\textrm{IC}_{50}}{1+ \\frac{[L]_{\\rm T} (y_0 + 2)}{2 K_{\\rm d} (y_0 + 1)} + y_0} - K_{\\rm d} \\left(\\frac{y_0}{y_0 + 2}\\right) \\;\\;\\;\\;\\mbox{(Eq.26; Munson\u2013Rodbard\u5f0f) }<br>\\end{equation}<\/p>\n\n\n\n<p>\\(y_0\\)\u304c\u975e\u5e38\u306b\u5c0f\u3055\u3051\u308c\u3070\u3001\u5f0f26\u306fCheng\u2013Prusoff\u5f0f\u3078\u3068\u5e30\u7740\u3059\u308b\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Munson\u2013Rodbard\u5f0f\u306e\u5c0e\u51fa<\/h4>\n\n\n\n<p>\\(K_1 = 1\/K_{\\rm d}\\), \\(K_2 = 1\/K_{\\rm i}\\) \u3068\u5b9a\u7fa9\u3059\u308b\u3002<br>\\begin{equation}<br>[RL] = K_1 [R] [L]\\;\\;\\;\\;\\mbox{(Eq.27)}<br>\\end{equation}<br>\\begin{equation}<br>[RI] = K_2 [R] [I]\\;\\;\\;\\;\\mbox{(Eq.28)}<br>\\end{equation}<br>\u4fdd\u5b58\u5247\u304b\u3089<br>\\begin{equation}<br>[L]_{\\rm T} = [RL] + [L]\\;\\;\\;\\;\\mbox{(Eq.29)}<br>\\end{equation}<br>\\begin{equation}<br>[I]_{\\rm T} = [RI] + [I]\\;\\;\\;\\;\\mbox{(Eq.30)}<br>\\end{equation}<br>\\begin{equation}<br>[R]_{\\rm T} = [RI] + [R] + [RL] = K_2 [R] [I] + [R] + K_1 [R] [L] = [R] (1+ K_1[L] + K_2 [I])\\;\\;\\;\\;\\mbox{(Eq.31)}<br>\\end{equation}<\/p>\n\n\n\n<p>\u963b\u5bb3\u5264\u304c\u5b58\u5728\u3057\u306a\u3044\u5834\u5408\u306850%\u963b\u5bb3\u6642\u306e\u6761\u4ef6\u3092\u8003\u3048\u308b\u3002<\/p>\n\n\n\n<p>\u963b\u5bb3\u5264\u304c\u5b58\u5728\u3057\u306a\u3044\u5834\u5408\u306e\u6bd4\u3092 \\([RL]_0\/[L]_0 = y_0\\) \u3068\u5b9a\u7fa9\u3059\u308b\u3068\u5f0f29\u304b\u3089\u3001<br>\\begin{equation}<br>[L]_{\\rm T} = [L]_0 (1 + y_0)\\;\\;\\;\\;\\mbox{(Eq.32)}<br>\\end{equation}<br>\\begin{equation}<br>[L]_0 =\\frac{[L]_{\\rm T}}{1 + y_0}\\;\\;\\;\\;\\mbox{(Eq.33)}<br>\\end{equation}<br>\u3057\u305f\u304c\u3063\u3066\u3001<br>\\begin{equation}<br>[RL]_0 = \\frac{ y_0 [L]_{\\rm T}}{1 + y_0}\\;\\;\\;\\;\\mbox{(Eq.34)}<br>\\end{equation}<\/p>\n\n\n\n<p>50%\u963b\u5bb3\u6642\u306f\u3001<br>\\begin{equation}<br>[RL]_{50} = \\frac{ y_0 [L]_{\\rm T}}{2 (1 + y_0)}\\;\\;\\;\\;\\mbox{(Eq.35)}<br>\\end{equation}<br>Eq.29\u304b\u3089\u3001<br>\\begin{equation}<br>[L]_{50} = [L]_{\\rm T} - [RL]_{50} = \\frac{ [L]_{\\rm T} (2 + y_0) }{2 (1 + y_0)}\\;\\;\\;\\;\\mbox{(Eq.36)}<br>\\end{equation}<\/p>\n\n\n\n<p>Eq.27\u304b\u308950%\u963b\u5bb3\u6642\u306efree\u306e\u30ec\u30bb\u30d7\u30bf\u30fc\u3092\u6c42\u3081\u308b\u3068\u3001<br>\\begin{equation}<br>[R]_{50} = \\frac{[RL]_{50}}{K_1 [L]_{50}} = \\frac{y_0}{K_1 (y_0 + 2)}\\;\\;\\;\\;\\mbox{(Eq.37)}<br>\\end{equation}<\/p>\n\n\n\n<p>Eq.28, 30\u304b\u3089\u3001<br>\\begin{equation}<br>\\textrm{IC}_{50} = [I]_{{\\rm T} 50} = [RI]_{50} + [I]_{50} = [I]_{50}(1+K_2 [R]_{50})\\;\\;\\;\\;\\mbox{(Eq.38)}<br>\\end{equation}<br>Eq.37\u3092Eq.38\u306b\u4ee3\u5165\u3059\u308b\u3068\u3001<br>\\begin{equation}<br>[I]_{50} = \\frac{\\textrm{IC}_{50}}{1+\\left(\\frac{K_2}{K_1}\\right)\\left(\\frac{y_0}{y_0+2}\\right)}\\;\\;\\;\\;\\mbox{(Eq.39)}<br>\\end{equation}<br>Eq.31\u3092 \\([R]\\) \u306b\u3064\u3044\u3066\u89e3\u3044\u3066Eq.27\u306b\u4ee3\u5165\u3059\u308b\u3068\u3001<br>\\begin{equation}<br>[RL] = \\frac{K_1 [R]_{\\rm T} [L] }{1+ K_1 [L] + K_2 [I]}\\;\\;\\;\\;\\mbox{(Eq.40)}<br>\\end{equation}<\/p>\n\n\n\n<p>\u963b\u5bb3\u5264\u304c\u5b58\u5728\u3057\u306a\u3044\u6642\u3001Eq.40\u306fEq.34, 33\u304b\u3089\u3001<br>\\begin{equation}<br>[R]_{\\rm T} = y_0 \\left(\\frac{1}{K_1} + \\frac{[L]_{\\rm T}}{1 + y_0}\\right)\\;\\;\\;\\;\\mbox{(Eq.41)}<br>\\end{equation}<\/p>\n\n\n\n<p>50%\u963b\u5bb3\u6642\u3001Eq.40\u306f\u3001<br>\\begin{equation}<br>[RL]_{50} = \\frac{K_1 [R]_{\\rm T} [L]_{50} }{1+ K_1 [L]_{50} + K_2 [I]_{50}}\\;\\;\\;\\;\\mbox{(Eq.42)}<br>\\end{equation}<\/p>\n\n\n\n<p>Eq.42\u3092\\(1\/K_2\\)\u306b\u3064\u3044\u3066\u89e3\u304f\u3002<\/p>\n\n\n\n<p>\\begin{equation} \\frac{1}{K_2} = \\frac{[I]_{50}}{\\frac{K_1[R]_{T}[L]_{50}}{[RL]_{50}} - K_1[L]_{50} - 1} \\end{equation}<\/p>\n\n\n\n<p>Eq.39\u304b\u3089<meta charset=\"utf-8\"> \\([I]_{50}\\)\u3092\u4ee3\u5165\u3057\u3066\u6574\u7406\u3059\u308b\u3002<\/p>\n\n\n\n<p>\\begin{equation} \\frac{1}{K_2} + \\frac{1}{K_1}\\left(\\frac{y_0}{y_0+2}\\right) = \\frac{\\mathrm{IC}_{50}}{\\frac{K_1[R]_{T}[L]_{50}}{[RL]_{50}} - K_1[L]_{50} - 1} \\end{equation}<\/p>\n\n\n\n<p>\u4e0a\u306e\u5f0f\u306e\u53f3\u8fba\u306e\u5206\u6bcd\u306b\u3001Eq.36\u304b\u3089\\([L]_{50}\\)\u3001Eq.41\u304b\u3089 \\([R]_{\\rm T}\\)\u3001\u305d\u3057\u3066 \\(\\frac{[L]_{50}}{[RL]_{50}} = \\frac{y_0+2}{y_0} \\) \u3092\u4ee3\u5165\u3059\u308b\u3068\u3001<\/p>\n\n\n\n<p>\\begin{equation} \\mbox{\u53f3\u8fba\u306e\u5206\u6bcd} = K_1 \\times y_0\\left(\\frac{1}{K_1} + \\frac{[L]_\\mathrm{T}}{y_0+1}\\right) \\times \\frac{y_0+2}{y_0} - K_1\\frac{[L]_\\mathrm{T}(y_0+2)}{2(y_0+1)} - 1 \\end{equation}<\/p>\n\n\n\n<p>\\begin{equation} = 2+ y_0 + K_1\\frac{[L]_\\mathrm{T}(y_0+2)}{y_0+1} - K_1\\frac{[L]_\\mathrm{T}(y_0+2)}{2(y_0+1)} - 1 \\end{equation}<\/p>\n\n\n\n<p>\\begin{equation} = 1+ K_1\\frac{[L]_\\mathrm{T}(y_0+2)}{2(y_0+1)} + y_0  \\end{equation}<\/p>\n\n\n\n<p>\u3057\u305f\u304c\u3063\u3066\u3001<br>\\begin{equation}<br>\\frac{1}{K_2} = \\frac{\\textrm{IC}_{50}}{1+ \\frac{[L]_{\\rm T} (y_0 + 2)}{2 \\left(\\frac{1}{K_1}\\right) (y_0 + 1)} + y_0} - \\left(\\frac{1}{K_1}\\right) \\left(\\frac{y_0}{y_0 + 2}\\right)\\;\\;\\;\\;\\mbox{(Eq.43)}<br>\\end{equation}<\/p>\n\n\n\n<p>\u6700\u5f8c\u306b\\(1\/K_2 = K_{\\rm i}\\), \\(1\/K_1 = K_{\\rm d}\\)\u3092\u623b\u3059\u3068Eq.26\u3068\u306a\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u8fd1\u4f3c\u3092\u4f7f\u308f\u305a\u306b1\u70b9\u304b\u3089Ki\u5024\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span style=\"font-weight: bold;\">Dandliker\u306e\u5f0f<\/span><\/h3>\n\n\n\n<p>\u963b\u5bb3\u5b9f\u9a13\u306e\u305d\u308c\u305e\u308c\u306e\u30c7\u30fc\u30bf\u70b9\u304b\u3089\\(K_{\\rm i}\\)\u3092\u7b97\u51fa\u3067\u304d\u308b (Dandliker, 1981)\u3002<\/p>\n\n\n\n<p>\\(\\chi = [RL]\/[L]\\) \u3068\u3059\u308b (\\([L]\\)\u306e\u5024\u306f \\([L] = [L]_{\\rm T} - [RL]\\) \u3068\u8a08\u7b97) \u3068\u3001<\/p>\n\n\n\n<p>\\begin{equation}<br>K_i = \\frac{[I]_{\\rm T} K_d \\chi}{[R]_{\\rm T} - \\frac{[L]_{\\rm T}\\chi}{1 + \\chi} - K_d \\chi} - K_d \\chi\\;\\;\\;\\;\\mbox{(Eq.44)}<br>\\end{equation}<\/p>\n\n\n\n<p>\u307e\u305f\u3001\\(f_b = [RL]\/[L]_{\\rm T}\\) \u3068\u3059\u308b\u3068\u3001\\(\\chi = f_b\/(1-f_b)\\) \u306a\u306e\u3067\u3001<\/p>\n\n\n\n<p>\\begin{equation}<br>K_{\\rm i} = \\frac{[I]_{\\rm T} K_{\\rm d} f_b}{[R]_{\\rm T}(1 - f_b) - K_{\\rm d} f_b - [L]_{\\rm T} f_b (1 - f_b)} - \\frac{K_{\\rm d} f_b}{ 1 - f_b}\\;\\;\\;\\;\\mbox{(Eq.45)}<br>\\end{equation}<\/p>\n\n\n\n<p>Eq.45\u306fHuang, 2003\u306e\u5f0f (11) \u3092\u5909\u5f62\u3057\u305f\u3082\u306e\u3067\u3059\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Dandliker\u306e\u5f0f\u306e\u5c0e\u51fa<\/h4>\n\n\n\n<p>\u5148\u7a0b\u3068\u540c\u69d8\u306b\u3001\\(K_1 = 1\/K_{\\rm d}\\), \\(K_2 = 1\/K_{\\rm i}\\)\u3068\u5b9a\u7fa9\u3059\u308b\u3002<br>\\begin{equation}<br>\\chi = \\frac{[RL]}{[L]} = K_1 ([R]_{\\rm T} - [RL] - [RI])\\;\\;\\;\\;\\mbox{(Eq.46)}<br>\\end{equation}<br>\\begin{equation}<br>\\frac{[RI]}{[I]} = K_2 ([R]_{\\rm T} - [RL] - [RI])\\;\\;\\;\\;\\mbox{(Eq.47)}<br>\\end{equation}<br>\\begin{equation}<br>[L]_{\\rm T} = [RL] + [L]\\;\\;\\;\\;\\mbox{(Eq.48)}<br>\\end{equation}<br>\\begin{equation}<br>[I]_{\\rm T} = [RI] + [I]\\;\\;\\;\\;\\mbox{(Eq.49)}<br>\\end{equation}<br>\\begin{equation}<br>[RL] =\\frac{[L]_{\\rm T}\\chi}{1 + \\chi}\\;\\;\\;\\;\\mbox{(Eq.50)}<br>\\end{equation}<br>\\begin{equation}<br>[L] =\\frac{[L]_{\\rm T}}{1 + \\chi}\\;\\;\\;\\;\\mbox{(Eq.51)}<br>\\end{equation}<br>Eq.46\u304b\u3089\u3001<br>\\begin{equation}<br>[RI] = [R]_{\\rm T} - [RL] - \\frac{\\chi}{K_1} = [R]_{\\rm T} - \\frac{[L]_{\\rm T}\\chi}{1 + \\chi} - \\frac{\\chi}{K_1}\\;\\;\\;\\;\\mbox{(Eq.52)}<br>\\end{equation}<\/p>\n\n\n\n<p>Eq.47\u3092 \\([I]\\) \u306b\u3064\u3044\u3066\u89e3\u304f\u3068<br>\\begin{equation}<br>[I] = \\frac{[RI]}{K_2} \\times \\frac{1}{[R]_{\\rm T} - [RL] - [RI]}\\;\\;\\;\\;\\mbox{(Eq.53)}<br>\\end{equation}<br>\\([RI] = [R]_{\\rm T} - [RL] - \\frac{\\chi}{K_1}\\)\u306a\u306e\u3067\u3001<br>\\begin{equation}<br>[I] = \\frac{[R]_{\\rm T} - [RL] - \\frac{\\chi}{K_1}}{K_2} \\times \\frac{1}{\\frac{\\chi}{K_1}} = \\frac{K_1}{K_2\\chi}\\left([R]_{\\rm T} - \\frac{[L]_{\\rm T}\\chi}{1 + \\chi} - \\frac{\\chi}{K_1}\\right)\\;\\;\\;\\;\\mbox{(Eq.54)}<br>\\end{equation}<br>Eq.52\u3068Eq.54\u3092Eq.49\u306b\u4ee3\u5165\u3059\u308b\u3068\u3001<br>\\begin{equation}<br>[I]_{\\rm T} = \\left(1 + \\frac{K_1}{K_2\\chi}\\right) \\left([R]_{\\rm T} - \\frac{[L]_{\\rm T}\\chi}{1 + \\chi} - \\frac{\\chi}{K_1}\\right)\\;\\;\\;\\;\\mbox{(Eq.55)}<br>\\end{equation}<\/p>\n\n\n\n<p>Eq.55\u3092\\(1\/K_2\\)\u306b\u3064\u3044\u3066\u89e3\u304f\u3068\u3001<br>\\begin{equation}<br>K_i = \\frac{1}{K_2} = \\frac{[I]_{\\rm T} K_d \\chi}{[R]_{\\rm T} - \\frac{[L]_{\\rm T}\\chi}{1 + \\chi} - K_d \\chi} - K_d \\chi\\;\\;\\;\\;\\mbox{(Eq.56)}<br>\\end{equation}<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">References<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Sharkey, N. A.; Blumberg, P. M. Highly lipophilic phorbol esters as inhibitors of specific [<sup>3<\/sup>H]phorbol 12,13-dibutyrate binding. <span style=\"font-style: italic;\">Cancer Res<\/span>. <span style=\"font-weight: bold;\">1985<\/span>, <span style=\"font-style: italic;\">45<\/span>, 19\u201324. [<a href=\"http:\/\/cancerres.aacrjournals.org\/content\/45\/1\/19.abstract\">URL<\/a>] [PMID]: <a href=\"https:\/\/www.ncbi.nlm.nih.gov\/pubmed\/3855281\/\">3855281<\/a>.<\/li>\n\n\n\n<li>Dandliker, W. B.; Hsu, M.-L.; Levin, J.; Rao, R. Equilibrium and kinetic inhibition assays based upon fluorescence polarization. <span style=\"font-style: italic;\">Methods Enzymol<\/span>. <span style=\"font-weight: bold;\">1981<\/span>, <span style=\"font-style: italic;\">74<\/span>, 3\u201328. DOI: <a href=\"http:\/\/dx.doi.org\/10.1016\/0076-6879(81)74003-5\">10.1016\/0076-6879(81)74003-5<\/a>. PMID:&nbsp;<a href=\"https:\/\/www.ncbi.nlm.nih.gov\/pubmed\/7321886\">7321886<\/a>.<\/li>\n\n\n\n<li>Goldstein, A.; Barrett, R. W. Ligand dissociation constants from competition binding assays: errors associated with ligand depletion. <span style=\"font-style: italic;\">Mol. Pharmacol<\/span>. <span style=\"font-weight: bold;\">1987<\/span>, <span style=\"font-style: italic;\">31<\/span>, 603\u2013609. [<a href=\"http:\/\/molpharm.aspetjournals.org\/content\/31\/6\/603.long\">URL<\/a>] PMID:&nbsp;<a href=\"https:\/\/www.ncbi.nlm.nih.gov\/pubmed\/3600604\">3600604<\/a>.<\/li>\n\n\n\n<li>Hulme, X. C.; Trevethick, M. A. Ligand binding assays at equilibrium: validation and interpretation. <span style=\"font-style: italic;\">Br. J. Pharmacol.<\/span> <span style=\"font-weight: bold;\">2010<\/span>, <span style=\"font-style: italic;\">161<\/span>, 1219\u20131237. DOI:&nbsp;<a href=\"http:\/\/dx.doi.org\/10.1111\/j.1476-5381.2009.00604.x\">10.1111\/j.1476-5381.2009.00604.<\/a>&nbsp;PMID:&nbsp;<a href=\"https:\/\/www.ncbi.nlm.nih.gov\/pubmed\/20132208\">20132208<\/a>.<\/li>\n\n\n\n<li>Huang, X. Equilibrium competition binding assay: inhibition mechanism from a single dose response. <span style=\"font-style: italic;\">J. Ther. Biol<\/span>. <span style=\"font-weight: bold;\">2003<\/span>, <span style=\"font-style: italic;\">225<\/span>, 369\u2013376. DOI:&nbsp;<a href=\"http:\/\/dx.doi.org\/10.1016\/S0022-5193(03)00265-0\">10.1016\/S0022-5193(03)00265-0<\/a>. PMID:&nbsp;<a href=\"https:\/\/www.ncbi.nlm.nih.gov\/pubmed\/14604589\">14604589<\/a>.<\/li>\n\n\n\n<li>Munson, P. J.; Rodbard, D. An exact correction to the Cheng-Prusoff correction. <span style=\"font-style: italic;\">J. Receptor Res<\/span>. <span style=\"font-weight: bold;\">1988<\/span>, <span style=\"font-style: italic;\">8<\/span>, 533\u2013546. DOI:&nbsp;<a href=\"http:\/\/dx.doi.org\/10.3109\/10799898809049010\">10.3109\/10799898809049010<\/a>. PMID:&nbsp;<a href=\"https:\/\/www.ncbi.nlm.nih.gov\/pubmed\/3385692\">3385692<\/a>.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u304a\u307e\u3051: \u5b9f\u969b\u306e\u5b9f\u9a13\u30c7\u30fc\u30bf\u306e\u51e6\u7406<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Low-affinity ligand<\/h3>\n\n\n\n<p><sup>3<\/sup>H\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\uff08\u6bd4\u6d3b\u602718.7 Ci\/mmol\uff09\u3068\u975e\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u3068\u306e\u7af6\u5408\u7d50\u5408\u8a66\u9a13\u3067\u5f97\u3089\u308c\u305f\u4ee5\u4e0b\u306e\u30c7\u30fc\u30bf\u3092\u51e6\u7406\u3057\u307e\u3059\u3002\u653e\u5c04\u6d3b\u6027\u306e\u5358\u4f4d\u306fdpm\uff08\u58ca\u5909\u6bce\u5206; Bq\u306f\u58ca\u5909\u6bce\u79d2\uff09\u3067\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-flexible-table-block-table is-style-stripes\"><table class=\"\"><tbody><tr><td style=\"border-color:#ffffff\">GROUP<\/td><td style=\"border-color:#ffffff\">log<sub>10<\/sub> [<em>I<\/em>]<sub>T<\/sub><\/td><td style=\"border-color:#ffffff\">pellet (dpm)<\/td><td style=\"border-color:#ffffff\">supernatant (dpm) (50 \u03bcL)<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Total binding<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">36758<\/td><td style=\"border-color:#ffffff\">16101<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Total binding<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">37325<\/td><td style=\"border-color:#ffffff\">17380<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Total binding<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">36584<\/td><td style=\"border-color:#ffffff\">16934<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Total binding<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">38455<\/td><td style=\"border-color:#ffffff\">15247<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Total binding<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">33998<\/td><td style=\"border-color:#ffffff\">16772<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Nonspecific binding<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">5592<\/td><td style=\"border-color:#ffffff\">20072<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Nonspecific binding<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">4794<\/td><td style=\"border-color:#ffffff\">18772<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-6.5<\/td><td style=\"border-color:#ffffff\">35734<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-6.5<\/td><td style=\"border-color:#ffffff\">35884<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-6.5<\/td><td style=\"border-color:#ffffff\">32866<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-6<\/td><td style=\"border-color:#ffffff\">33393<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-6<\/td><td style=\"border-color:#ffffff\">33204<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-6<\/td><td style=\"border-color:#ffffff\">34506<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-5.5<\/td><td style=\"border-color:#ffffff\">28644<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-5.5<\/td><td style=\"border-color:#ffffff\">31701<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-5.5<\/td><td style=\"border-color:#ffffff\">30276<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-5<\/td><td style=\"border-color:#ffffff\">22413<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-5<\/td><td style=\"border-color:#ffffff\">22516<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-5<\/td><td style=\"border-color:#ffffff\">21133<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-4.5<\/td><td style=\"border-color:#ffffff\">12318<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-4.5<\/td><td style=\"border-color:#ffffff\">12711<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-4.5<\/td><td style=\"border-color:#ffffff\">11368<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>supernatant\u306e\u5024\u306b437\/50\u3092\u639b\u3051\u3066\u3001\u4e0a\u6e05\u5168\u4f53\u306e\u653e\u5c04\u6d3b\u6027\u306b\u5909\u63db\u3059\u308b\u3002<\/li>\n\n\n\n<li>\u5168\u653e\u5c04\u6d3b\u6027 = Total binding\u7fa4\u306epellet + supernatant \uff08\u5168\u4f53\uff09\u3001\u3092\u8a08\u7b97\u3059\u308b\u3002<\/li>\n\n\n\n<li>Nonspecific binding\u7fa4\u306epellet\u3092supernatant\uff08\u5168\u4f53\uff09\u3067\u5272\u3063\u3066\u3001\u975e\u7279\u7570\u7684\u5438\u7740\u306e\u5206\u914d\u4fc2\u6570 <em>k<\/em> \u3092\u8a08\u7b97\u3059\u308b: <em>k<\/em> = 0.0296\u3002<\/li>\n\n\n\n<li>Total binding\u7fa4\u306especific binding = pellet \u2212 <em>k<\/em> \u00d7 supernatant\uff08\u5168\u4f53\uff09\u3001\u3092\u8a08\u7b97\u3059\u308b\u3002<\/li>\n\n\n\n<li>Unlabeled ligand\u7fa4\u306especific binding = pellet \u2212 <em>k<\/em> \u00d7 (\u5168\u653e\u5c04\u6d3b\u6027 \u2212 pellet) \u3092\u8a08\u7b97\u3059\u308b\u3002 <\/li>\n\n\n\n<li>\u653e\u5c04\u6d3b\u6027 (dpm) \u3092\u30c6\u30b9\u30c8\u30c1\u30e5\u30fc\u30d6\u5185\u306e\u30e2\u30eb\u6fc3\u5ea6 (nM) \u306b\u5909\u63db\u3059\u308b\u3002\u4fc2\u6570 \\(N = \\frac{1}{60} \\times \\frac{1}{3.7 \\times 10^{10}} \\times \\frac{1}{\\mbox{\u6bd4\u6d3b\u6027 (Ci\/mmol)}} \\times \\frac{1}{10^3} \\times \\frac{1}{250 \\times 10^{-6}} \\times 10^9\\)<\/li>\n\n\n\n<li>Unlabeled ligand\u7fa4\u306e\u305d\u308c\u305e\u308c\u306e\u30c7\u30fc\u30bf\u306b\u3064\u3044\u3066 <em>\u03b8<\/em> = pellet (nM) \/ \u3008Total binding\u7fa4\u306especific binding\uff08[RL]<sub>0<\/sub>\uff09\u306e\u5e73\u5747\u5024\u3009\u3092\u8a08\u7b97\u3059\u308b\u3002<\/li>\n\n\n\n<li>\\(\\log_{10} \\{\\theta\/(1 - \\theta)\\}\\) \u3092\u8a08\u7b97\u3059\u308b\u3002<\/li>\n<\/ol>\n\n\n\n<p><strong>\u51e6\u7406\u3057\u305f\u30c7\u30fc\u30bf<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-flexible-table-block-table is-style-stripes\"><table class=\"\"><tbody><tr><td style=\"border-color:#ffffff\">GROUP<\/td><td style=\"border-color:#ffffff\">log<sub>10<\/sub> [<em>I<\/em>]<sub>T<\/sub><\/td><td style=\"border-color:#ffffff\">bound (nM)<\/td><td style=\"border-color:#ffffff\">free (nM)<\/td><td style=\"border-color:#ffffff\"><em>\u03b8<\/em><\/td><td style=\"border-color:#ffffff\">log<sub>10<\/sub> {<em>\u03b8<\/em>\/(1 \u2212 <em>\u03b8<\/em>)}<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Total binding\uff08\u5e73\u5747\uff09<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">3.105 ([<em>RL<\/em>]<sub>0<\/sub>)<\/td><td style=\"border-color:#ffffff\">13.88 ([<em>L<\/em>]<sub>0<\/sub>)<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-6.5<\/td><td style=\"border-color:#ffffff\">3.017<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">0.9715<\/td><td style=\"border-color:#ffffff\">1.533<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-6.5<\/td><td style=\"border-color:#ffffff\">3.032<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">0.9763<\/td><td style=\"border-color:#ffffff\">1.615<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-6.5<\/td><td style=\"border-color:#ffffff\">2.732<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">0.8798<\/td><td style=\"border-color:#ffffff\">0.865<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-6<\/td><td style=\"border-color:#ffffff\">2.785<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">0.8967<\/td><td style=\"border-color:#ffffff\">0.939<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-6<\/td><td style=\"border-color:#ffffff\">2.766<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">0.8907<\/td><td style=\"border-color:#ffffff\">0.911<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-6<\/td><td style=\"border-color:#ffffff\">2.895<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">0.9323<\/td><td style=\"border-color:#ffffff\">1.139<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-5.5<\/td><td style=\"border-color:#ffffff\">2.313<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">0.7448<\/td><td style=\"border-color:#ffffff\">0.465<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-5.5<\/td><td style=\"border-color:#ffffff\">2.616<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">0.8426<\/td><td style=\"border-color:#ffffff\">0.729<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-5.5<\/td><td style=\"border-color:#ffffff\">2.475<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">0.7970<\/td><td style=\"border-color:#ffffff\">0.594<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-4.5<\/td><td style=\"border-color:#ffffff\">1.694<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">0.5456<\/td><td style=\"border-color:#ffffff\">0.079<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-4.5<\/td><td style=\"border-color:#ffffff\">1.704<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">0.5489<\/td><td style=\"border-color:#ffffff\">0.085<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-4.5<\/td><td style=\"border-color:#ffffff\">1.567<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">0.5047<\/td><td style=\"border-color:#ffffff\">0.008<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-4<\/td><td style=\"border-color:#ffffff\">0.692<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">0.2228<\/td><td style=\"border-color:#ffffff\">-0.543<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-4<\/td><td style=\"border-color:#ffffff\">0.731<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">0.2354<\/td><td style=\"border-color:#ffffff\">-0.512<\/td><\/tr><tr><td style=\"border-color:#ffffff\">Unlabeled ligand (I)<\/td><td style=\"border-color:#ffffff\">-4<\/td><td style=\"border-color:#ffffff\">0.698<\/td><td style=\"border-color:#ffffff\">\u2014<\/td><td style=\"border-color:#ffffff\">0.1924<\/td><td style=\"border-color:#ffffff\">-0.623<\/td><\/tr><\/tbody><\/table><figcaption><em>K<\/em><sub>d<\/sub> = 0.53 nM\u3002\u305d\u306e\u4ed6\u306e\u8a08\u7b97\u5024\uff08\u5358\u4f4d\u306fnM\uff09: [<em>L<\/em>]<sub>T<\/sub> = 17.41; [<em>L<\/em>]*<sub>T<\/sub> = 16.90; [<em>R<\/em>]<sub>T<\/sub> = 3.224.<\/figcaption><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u95a2\u6570\u306b\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u3057\u3066IC<sub>50<\/sub>\u3092\u63a8\u5b9a\u3014\u63a8\u5968\u3015<\/h4>\n\n\n\n<pre class=\"prettyprint\">logIT &lt;- c(-6.5,-6.5,-6.5,-6,-6,-6,-5.5,-5.5,-5.5,-5,-5,-5,-4.5,-4.5,-4.5)\ntheta &lt;- c(0.9715, 0.9763, 0.8798, 0.8967, 0.8907, 0.9323, 0.7448, 0.8426, 0.7970, 0.5456, 0.5489, 0.5047, 0.2228, 0.2354, 0.1924)\nresult &lt;- nls(theta~1&#47;(1+exp(a*log(10)*(logIT - logIC50))),start = c(logIC50=-5, a=1))\nsummary(result)\n<\/pre>\n<p><b>Output<\/b>:<\/p>\n<pre class=\"prettyprint\">\nFormula: theta ~ 1&#47;(1 + exp(a * log(10) * (logIT - logIC50)))\n\nParameters:\n        Estimate Std. Error t value Pr(&gt;|t|)    \nlogIC50 -4.97382    0.02644 -188.15  &lt; 2e-16 ***\na        1.07378    0.06989   15.37 1.03e-09 ***\n---\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n\nResidual standard error: 0.04024 on 13 degrees of freedom\n\nNumber of iterations to convergence: 6 \nAchieved convergence tolerance: 1.317e-06\n<\/pre>\n<pre class=\"prettyprint\">confint(result, level=0.95)\n<\/pre>\n<p><b>Output<\/b>:<\/p>\n<pre class=\"prettyprint\">\n              2.5%     97.5%\nlogIC50 -5.0301661 -4.916613\na        0.9269206  1.247572\n<\/pre>\n\n\n\n<p>\u53ef\u8996\u5316:<\/p>\n\n\n\n<pre class=\"prettyprint\">concpre = seq(-8.5,-3.5, length=100)\nplot(theta~logIT,xlim=c(-10,-3.5),ylim=c(0,1))\nlines(concpre, predict(result, newdata=list(logIT=concpre)))\n<\/pre>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"966\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Nonlinear_low-1024x966.png\" alt=\"\" class=\"wp-image-6799\" style=\"width:348px;height:auto\" srcset=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Nonlinear_low-1024x966.png 1024w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Nonlinear_low-300x283.png 300w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Nonlinear_low-768x724.png 768w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Nonlinear_low.png 1442w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p>\u63a8\u5b9aIC<sub>50<\/sub>\u5024\u306f10,621 nM\uff0895%CI: 9,329\u201312,117\uff09\u3001\u30d2\u30eb\u4fc2\u6570\u306f1.07\u3060\u3063\u305f\u3002<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><em>K<\/em><sub>i<\/sub>\u3078\u306e\u5909\u63db<\/h5>\n\n\n\n<p>\u975e\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u306b\u3064\u3044\u3066\u3082 [<sup>3<\/sup>H]PDBu\u3068\u540c\u3058\u5206\u914d\u4fc2\u6570\u3067\u975e\u7279\u7570\u7684\u7d50\u5408\u304c\u8d77\u3053\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3002\u3059\u308b\u3068\u3001<\/p>\n\n\n\n<p>$$ \\mathrm{IC}_{50} = (1 + k) [I]_{50} + [RI]_{50} $$<\/p>\n\n\n\n<p>$$ [I]_{50} = \\frac{1}{1+ k} (\\mathrm{IC}_{50}  - [RI]_{50}) $$<\/p>\n\n\n\n<p>\u306a\u306e\u3067\u3001\\(\\mathrm{IC}_{50}\\)\u3092\\(K_\\mathrm{i}\\) \u306b\u5909\u63db\u3059\u308b\u4ee5\u4e0b\u306e\u53b3\u5bc6\u306a\u88dc\u6b63\u5f0f\u304c\u5f97\u3089\u308c\u308b\u3002<\/p>\n\n\n\n<p>$$ K_{\\rm i} = \\frac{\\frac{1}{1 + k} \\left[\\mathrm{IC}_{50} - \\left( 1 - \\frac{1}{2} \\frac{[L]_0}{[L]_{50}} \\right)[R]_{\\mathrm{T}} - \\left( \\frac{[L]_0}{[L]_{50}} - 1\\right) \\frac{[RL]_{0}}{2} \\right] }{2\\frac{[L]_{50}}{[L]_0} - 1 + \\frac{[L]_{50}}{K_{\\rm d}}} $$<\/p>\n\n\n\n<p>\u3053\u306e\u5834\u5408\u3001\u975e\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u306e\u89aa\u548c\u6027\u304c\u5f31\u304f\u3001\\(\\mathrm{IC}_{50} \\gg [RI]_{50}\\)\u304c\u6210\u308a\u7acb\u3064\u306e\u3067\u3001 \u4ee5\u4e0b\u306e\u8fd1\u4f3c\u304c\u6210\u308a\u7acb\u3064\u3002<\/p>\n\n\n\n<p>$$ [I]_{50} \\simeq \\frac{1}{1+ k} \\mathrm{IC}_{50} $$<\/p>\n\n\n\n<p>$$ K_{\\rm i} = \\frac{\\frac{1}{1 + k} \\mathrm{IC}_{50} }{2\\frac{[L]_{50}}{[L]_0} - 1 + \\frac{[L]_{50}}{K_{\\rm d}}} $$<\/p>\n\n\n\n<p>\u53b3\u5bc6\u306a\u5f0f\u3067\u5f97\u3089\u308c\u305f\\(K_\\mathrm{i}\\) \u306f <strong>340.6 nM<\/strong>\uff0895% CI: 299.1\u2013388.6\uff09\u3060\u3063\u305f\u3002\u8fd1\u4f3c\u5f0f\u3067\u5f97\u3089\u308c\u305f\\(K_\\mathrm{i}\\) \u306f <strong>340.7 nM<\/strong>\u3067\u3042\u308a\u3001\u9055\u3044\u304c\u306a\u3044\u3053\u3068\u304c\u5206\u304b\u3063\u305f\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">log<sub>10<\/sub> {<em>\u03b8<\/em>\/(1 \u2212 <em>\u03b8<\/em>)} \u5909\u63db\u304b\u3089\u7dda\u5f62\u56de\u5e30\u3067IC<sub>50<\/sub>\u3092\u63a8\u5b9a\u3014\u6b21\u306b\u63a8\u5968 \u203bMicrosoft Excel\u3057\u304b\u4f7f\u3048\u306a\u3044\u6642\u3015<\/h4>\n\n\n\n<p><strong>5\u3064\u306e\u6fc3\u5ea6\u5168\u3066\u3092\u4f7f\u7528<\/strong><\/p>\n\n\n\n<pre class=\"prettyprint\">logIT &lt;- c(-6.5,-6.5,-6.5,-6,-6,-6,-5.5,-5.5,-5.5,-5,-5,-5,-4.5,-4.5,-4.5)\nlogit &lt;- c(1.533, 1.615, 0.865, 0.939, 0.911, 1.139, 0.465, 0.729, 0.594, 0.079, 0.085, 0.008, -0.543, -0.512, -0.623)\nresult_lm &lt;- lm(logit ~ logIT)\nsummary(result_lm)\n<\/pre>\n<p><b>Output<\/b>:<\/p>\n<pre class=\"prettyprint\">\nCall:\nlm(formula = logit ~ logIT)\n\nResiduals:\n     Min       1Q   Median       3Q      Max \n-0.56720 -0.04945 -0.00430  0.10460  0.24340 \n\nCoefficients:\n            Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) -4.72070    0.40386  -11.69 2.86e-08 ***\nlogIT       -0.94660    0.07283  -13.00 7.98e-09 ***\n---\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n\nResidual standard error: 0.1995 on 13 degrees of freedom\nMultiple R-squared:  0.9285,\tAdjusted R-squared:  0.923 \nF-statistic: 168.9 on 1 and 13 DF,  p-value: 7.975e-09\n<\/pre>\n\n\n\n<p><strong>\u9ad8\u6fc3\u5ea6\u5074\u306e3\u3064\u306e\u6fc3\u5ea6\u3092\u4f7f\u7528<\/strong><\/p>\n\n\n\n<pre class=\"prettyprint\">logIT_a &lt;- c(-5.5,-5.5,-5.5,-5,-5,-5,-4.5,-4.5,-4.5)\nlogit_a &lt;- c(0.465, 0.729, 0.594, 0.079, 0.085, 0.008, -0.543, -0.512, -0.623)\nresult_lm_a &lt;- lm(logit_a ~ logIT_a)\nsummary(result_lm_a)\n<\/pre>\n<p><b>Output<\/b>:<\/p>\n<pre class=\"prettyprint\">\nCall:\nlm(formula = logit_a ~ logIT_a)\n\nResiduals:\n      Min        1Q    Median        3Q       Max \n-0.144000 -0.023333  0.003333  0.047667  0.120000 \n\nCoefficients:\n            Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept)  -5.7453     0.3396  -16.92 6.18e-07 ***\nlogIT_a      -1.1553     0.0677  -17.07 5.82e-07 ***\n---\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n\nResidual standard error: 0.08292 on 7 degrees of freedom\nMultiple R-squared:  0.9765,\tAdjusted R-squared:  0.9732 \nF-statistic: 291.2 on 1 and 7 DF,  p-value: 5.819e-07\n<\/pre>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"970\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Linear_low-1024x970.png\" alt=\"\" class=\"wp-image-6800\" style=\"aspect-ratio:1.0556669804756251;width:323px;height:auto\" srcset=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Linear_low-1024x970.png 1024w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Linear_low-300x284.png 300w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Linear_low-768x728.png 768w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/Linear_low.png 1444w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><strong>\u9ed2\u7dda\uff08\u6fc3\u5ea65\u70b9\uff09<\/strong>: \\( y = -0.94660 x - 4.72070\\). \\(R^2 = 0.929\\). log<sub>10<\/sub> IC<sub>50<\/sub> = -4.72070\/0.94660 = -4.987006\u3002nM\u306b\u5909\u63db\u3059\u308b\u3068IC<sub>50<\/sub> = <strong>10,304 nM<\/strong>\u3002<\/p>\n\n\n\n<p><strong>\u8d64\u7dda\uff08\u6fc3\u5ea63\u70b9\uff09<\/strong>: \\( y = -1.1553 x - 5.7453\\). \\(R^2 = 0.977\\). log<sub>10<\/sub> IC<sub>50<\/sub> = -5.7453\/1.1553 = -4.972994\u3002nM\u306b\u5909\u63db\u3059\u308b\u3068IC<sub>50<\/sub> = <strong>10,642 nM<\/strong>\u3002<\/p>\n\n\n\n<p>\u30c7\u30fc\u30bf\u6570\u304c\u5c11\u306a\u3044\u6fc3\u5ea63\u70b9\u304b\u3089\u63a8\u5b9a\u3057\u305fIC<sub>50<\/sub>\u5024\u306e\u65b9\u304c\u3001\u975e\u7dda\u5f62\u56de\u5e30\u304b\u3089\u63a8\u5b9a\u3057\u305fIC<sub>50<\/sub>\u5024\u306b\u8fd1\u3044\u7d50\u679c\u304c\u5f97\u3089\u308c\u305f\u3002\u7dda\u5f62\u5909\u63db\u3059\u308b\u3068\u30b7\u30b0\u30e2\u30a4\u30c9\u306e\u88fe\u306e\u65b9\u306e\u30c7\u30fc\u30bf\u70b9\u3092\u904e\u5927\u8a55\u4fa1\u3057\u3066\u3057\u307e\u3046\u3053\u3068\u304c\u5206\u304b\u308b\u3002<\/p>\n\n\n\n<p>\u524d\u7bc0\u3068\u540c\u3058\u8fd1\u4f3c\u5f0f\u3067\u5909\u63db\u3057\u305f<em>K<\/em><sub>i<\/sub> \u306f\u6fc3\u5ea65\u70b9\u304b\u3089\u304c<strong>330.5 nM<\/strong>\u3001\u6fc3\u5ea65\u70b9\u304b\u3089\u304c<strong>341.3 n<\/strong>M\u3060\u3063\u305f\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">GraphPad Prism\u306e\u65b9\u6cd5<\/h4>\n\n\n\n<p>\u53c2\u8003: <a href=\"https:\/\/www.graphpad.com\/guides\/prism\/latest\/curve-fitting\/reg_one_site_accounting_for_depletion.htm\" title=\"\">Equation: One site - Ligand depletion \u2014 GraphPad Prism 10<\/a><\/p>\n\n\n\n<p>\u6709\u511f\u306e\u7d71\u8a08\u89e3\u6790\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2<a href=\"https:\/\/www.graphpad.com\/features\" title=\"\">GraphPad Prism 10<\/a>\u306b\u5b9f\u88c5\u3055\u308c\u3066\u3044\u308b\u65b9\u6cd5\u306b\u5247\u3063\u3066\u89e3\u6790\u3092\u884c\u3063\u3066\u307f\u307e\u3057\u305f\uff08\u653e\u5c04\u6d3b\u6027\u306e\u5358\u4f4d\u306fCPM\u3067\u306f\u306a\u304fDPM\u3092\u4f7f\u7528\uff09\u3002\"One site - Ligand depletion\" \u30e2\u30c7\u30eb\u306f\u3001\u904a\u96e2\u578b\u653e\u5c04\u30ea\u30ac\u30f3\u30c9\u6fc3\u5ea6 \u2252 \u5168\u653e\u5c04\u30ea\u30ac\u30f3\u30c9\u6fc3\u5ea6\u3001\u306e\u8fd1\u4f3c\u304c\u4f7f\u3048\u306a\u3044\u5834\u5408\u306b\u9069\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u57fa\u672c\u7684\u306b\u306f\u300c\u7d50\u5408\u963b\u5bb3\u66f2\u7dda\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u300d\u7bc0\u3067\u793a\u3057\u305f\u5f0f<\/p>\n\n\n\n<p>$$ [RL] = \\frac{1}{2}\\left\\{\\left[[R]_{\\rm T} + [L]_{\\rm T} + \\left(1+\\frac{[I]}{K_{\\rm i}}\\right)K_{\\rm d}\\right] - \\sqrt{\\left[[R]_{\\rm T} + [L]_{\\rm T} + \\left(1+\\frac{[I]}{K_{\\rm i}}\\right)K_{\\rm d}\\right]^2 - 4[R]_{\\rm T}[L]_{\\rm T}}\\right\\} $$<\/p>\n\n\n\n<p>\u306b\u5bfe\u3057\u3066\u3001\u975e\u7279\u7570\u7684\u7d50\u5408\u3092\u8003\u616e\u3057\u3066\u653e\u5c04\u6d3b\u6027\u306fCPM\u5358\u4f4d\u306e\u307e\u307e\u975e\u7dda\u5f62\u56de\u5e30\u3092\u884c\u3063\u3066\u3044\u307e\u3059\u3002Total binding\u7fa4\u3068non-specific binding\u7fa4\u306e\u653e\u5c04\u6d3b\u6027\u306e\u5024\u306f\u4f7f\u7528\u3057\u307e\u305b\u3093\u3002\u3053\u3053\u3067\u306fCPM\u3067\u306f\u306a\u304fDPM\u5358\u4f4d\u3092\u4f7f\u7528\u3057\u3066\u3044\u308b\u306e\u3067\u6bd4\u6d3b\u6027SpAct\u306e\u5358\u4f4d\u306f dpm\/fmol \u3067\u3059\u3002<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">\u30d1\u30e9\u30e1\u30fc\u30bf<\/h5>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>Hot<\/em> = [<em>L<\/em>]<sub>T<\/sub> = 17.41 [nM] = 180718 [DPM]<\/li>\n\n\n\n<li><em>KdNM<\/em> = <em>K<\/em><sub>d<\/sub> = 0.53 [nM]<\/li>\n\n\n\n<li><em>SpAct<\/em> = 18.7 [Ci\/mmol] = 41.514 [dpm\/fmol]<\/li>\n\n\n\n<li><em>Vol<\/em> = 0.25 [mL]<\/li>\n<\/ul>\n\n\n\n<h5 class=\"wp-block-heading\">\u30e2\u30c7\u30eb<\/h5>\n\n\n\n<p>\\(KdDPM=KdNM * SpAct * Vol * 1000&nbsp;\\)<\/p>\n\n\n\n<p>\\(R = 1 + NS\\) ; <\/p>\n\n\n\n<p>\\(S=[1+10^{(X-LogKi)}] * KdDPM+Hot\\)<\/p>\n\n\n\n<p>\\(a=-1 * R\\)<\/p>\n\n\n\n<p>\\(b=R * S+NS * Hot&nbsp;+&nbsp;Bmax\\)<\/p>\n\n\n\n<p>\\(c=&nbsp;-1*Hot*(S*NS&nbsp;+&nbsp;Bmax) \\)<\/p>\n\n\n\n<p>\\(Y=&nbsp;\\frac{-b&nbsp;+&nbsp;\\sqrt{b^2-4*a*c}}{2*a} \\)<\/p>\n\n\n\n<pre class=\"prettyprint lang-r\">X &lt;- c(-6.5,-6.5,-6.5,-6,-6,-6,-5.5,-5.5,-5.5,-5,-5,-5,-4.5,-4.5,-4.5)\nY &lt;- c(35734, 35884, 32866, 33393, 33204, 34506, 28643, 31701, 30276, 22413, 22516, 21133, 12318, 12711, 11368)\nHot &lt;- 180718\nKdNM &lt;- 0.53\nSpAct &lt;- 41.514\nVol &lt;- 0.25\nbinding_model &lt;- function(X, LogKi, Bmax, NS, Hot, KdNM, SpAct, Vol) {\n      KdDPM &lt;- KdNM * SpAct * Vol * 1000\n      R &lt;- 1 + NS\n      S &lt;- (1 + 10^(X - LogKi)) * KdDPM + Hot\n      a &lt;- -R\n      b &lt;- R * S + NS * Hot + Bmax\n      c &lt;- -Hot * (S * NS + Bmax)\n      return((-b + sqrt(b^2 - 4 * a * c)) &#47; (2 * a))\n}\nresult_GP &lt;- nls(\n     Y ~ binding_model(X, LogKi, Bmax, NS, Hot, KdNM, SpAct, Vol),\n     start = list(\n         LogKi = -5.0, \n         Bmax  = 30000,\n         NS    = 0.03\n     ),\n     algorithm = &#34;port&#34;\n)\nsummary(result_GP)\n<\/pre>\n<p><b>Output<\/b>:<\/p>\n<pre class=\"prettyprint\">\nFormula: Y ~ binding_model(X, LogKi, Bmax, NS, Hot, KdNM, SpAct, Vol)\n\nParameters:\n        Estimate Std. Error t value Pr(&gt;|t|)    \nLogKi -6.212e+00  9.316e-02 -66.685  &lt; 2e-16 ***\nBmax   3.920e+04  2.644e+03  14.824 4.45e-09 ***\nNS    -1.403e-02  1.919e-02  -0.731    0.479    \n---\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n\nResidual standard error: 1089 on 12 degrees of freedom\n\nAlgorithm &#34;port&#34;, convergence message: relative convergence (4)\n<\/pre>\n\n\n\n<p>\u7d50\u679c\u306f <em>K<\/em><sub>i<\/sub> = 10^(-6.212 + 9) = 614 [nM]\u3001Bmax = 39,200\u3001NS = 0.01403\u3002\u5f93\u6765\u901a\u308aIC<sub>50<\/sub>\u5024\u304b\u3089\u5909\u63db\u3057\u305f\u6642\u3088\u308a\u3082<em>K<\/em><sub>i<\/sub>\u304c2\u500d\u307b\u3069\u5927\u304d\u3044\u3002<\/p>\n\n\n\n<p>\u53ef\u8996\u5316:<\/p>\n\n\n\n<pre class=\"prettyprint\">concpre = seq(-9.5,-3.5, length=100)\nplot(Y~X,xlim=c(-10,-3.5),ylim=c(0,50000))\nlines(concpre, predict(result_GP, newdata=list(X=concpre)))\n<\/pre>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"955\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/GraphPad_low-1024x955.png\" alt=\"\" class=\"wp-image-6803\" style=\"aspect-ratio:1.072262002114207;width:340px;height:auto\" srcset=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/GraphPad_low-1024x955.png 1024w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/GraphPad_low-300x280.png 300w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/GraphPad_low-768x716.png 768w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/GraphPad_low.png 1446w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p>\u5de6\u53f3\u3068\u3082\u306bPlateau\u9818\u57df\u306e\u30c7\u30fc\u30bf\u70b9\u304c\u306a\u3044\u3068Prism\u306e\u30c7\u30fc\u30bf\u51e6\u7406\u3067\u306f\u3046\u307e\u304f\u3044\u304b\u306a\u3044\u3053\u3068\u304c\u5206\u304b\u3063\u305f\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Tight-binding ligand<\/h3>\n\n\n\n<p><sup>3<\/sup>H\u6a19\u8b58\u30ea\u30ac\u30f3\u30c9\u306e\u6bd4\u6d3b\u6027\u306f12.31 Ci\/mmol\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td>GROUP<\/td><td>log<sub>10<\/sub> [<em>I<\/em>]<sub>T<\/sub><\/td><td>pellet (dpm)<\/td><td>supernatant (dpm) (50 \u03bcL)<\/td><\/tr><tr><td>Total binding<\/td><td>\u2014<\/td><td>38985<\/td><td>10382<\/td><\/tr><tr><td>Total binding<\/td><td>\u2014<\/td><td>38931<\/td><td>10907<\/td><\/tr><tr><td>Total binding<\/td><td>\u2014<\/td><td>38495<\/td><td>9242<\/td><\/tr><tr><td>Total binding<\/td><td>\u2014<\/td><td>39034<\/td><td>10287<\/td><\/tr><tr><td>Nonspecific binding<\/td><td>\u2014<\/td><td>3629<\/td><td>14208<\/td><\/tr><tr><td>Nonspecific binding<\/td><td>\u2014<\/td><td>3448<\/td><td>13194<\/td><\/tr><tr><td>Unlabeled ligand (I)<\/td><td>-8.5<\/td><td>26327<\/td><td>\u2014<\/td><\/tr><tr><td>Unlabeled ligand (I)<\/td><td>-8.5<\/td><td>26072<\/td><td>\u2014<\/td><\/tr><tr><td>Unlabeled ligand (I)<\/td><td>-8.5<\/td><td>25105<\/td><td>\u2014<\/td><\/tr><tr><td>Unlabeled ligand (I)<\/td><td>-8<\/td><td>13168<\/td><td>\u2014<\/td><\/tr><tr><td>Unlabeled ligand (I)<\/td><td>-8<\/td><td>11354<\/td><td>\u2014<\/td><\/tr><tr><td>Unlabeled ligand (I)<\/td><td>-8<\/td><td>11917<\/td><td>\u2014<\/td><\/tr><tr><td>Unlabeled ligand (I)<\/td><td>-7.5<\/td><td>6314<\/td><td>\u2014<\/td><\/tr><tr><td>Unlabeled ligand (I)<\/td><td>-7.5<\/td><td>6446<\/td><td>\u2014<\/td><\/tr><tr><td>Unlabeled ligand (I)<\/td><td>-7.5<\/td><td>5829<\/td><td>\u2014<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>\u51e6\u7406\u3057\u305f\u30c7\u30fc\u30bf<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td>GROUP<\/td><td>log<sub>10<\/sub> [<em>I<\/em>]<sub>T<\/sub><\/td><td>bound (nM)<\/td><td>free (nM)<\/td><td><em>\u03b8<\/em><\/td><td>log<sub>10<\/sub> {<em>\u03b8<\/em>\/(1 \u2212 <em>\u03b8<\/em>)}<\/td><\/tr><tr><td>Total binding\uff08\u5e73\u5747\uff09<\/td><td>\u2014<\/td><td>5.302  ([<em>RL<\/em>]<sub>0<\/sub>)<\/td><td>13.05 ([<em>L<\/em>]<sub>0<\/sub>)<\/td><td>\u2014<\/td><td>\u2014<\/td><\/tr><tr><td>Unlabeled ligand (I)<\/td><td>-8.5<\/td><td>3.413<\/td><td>\u2014<\/td><td>0.6438<\/td><td>0.257<\/td><\/tr><tr><td>Unlabeled ligand (I)<\/td><td>-8.5<\/td><td>3.375<\/td><td>\u2014<\/td><td>0.6365<\/td><td>0.243<\/td><\/tr><tr><td>Unlabeled ligand (I)<\/td><td>-8.5<\/td><td>3.229<\/td><td>\u2014<\/td><td>0.6090<\/td><td>0.193<\/td><\/tr><tr><td>Unlabeled ligand (I)<\/td><td>-8<\/td><td>1.430<\/td><td>\u2014<\/td><td>0.2698<\/td><td>-0.432<\/td><\/tr><tr><td>Unlabeled ligand (I)<\/td><td>-8<\/td><td>1.157<\/td><td>\u2014<\/td><td>0.2182<\/td><td>-0.554<\/td><\/tr><tr><td>Unlabeled ligand (I)<\/td><td>-8<\/td><td>1.242<\/td><td>\u2014<\/td><td>0.2342<\/td><td>-0.515<\/td><\/tr><tr><td>Unlabeled ligand (I)<\/td><td>-7.5<\/td><td>0.397<\/td><td>\u2014<\/td><td>0.0750<\/td><td>-1.091<\/td><\/tr><tr><td>Unlabeled ligand (I)<\/td><td>-7.5<\/td><td>0.417<\/td><td>\u2014<\/td><td>0.0787<\/td><td>-1.068<\/td><\/tr><tr><td>Unlabeled ligand (I)<\/td><td>-7.5<\/td><td>0.324<\/td><td>\u2014<\/td><td>0.0612<\/td><td>-1.186<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\"><em>K<\/em><sub>d<\/sub> = 0.53 nM\u3002\u305d\u306e\u4ed6\u306e\u8a08\u7b97\u5024\uff08\u5358\u4f4d\u306fnM\uff09: [<em>L<\/em>]<sub>T<\/sub> = 18.74; [<em>L<\/em>]*<sub>T<\/sub> = 18.20; [<em>R<\/em>]<sub>T<\/sub> = 5.52.<\/figcaption><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u95a2\u6570\u306b\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u3057\u3066IC<sub>50<\/sub>\u3092\u63a8\u5b9a\u3014\u63a8\u5968\u3015<\/h4>\n\n\n\n<pre class=\"prettyprint\">logIT &lt;- c(-8.5,-8.5,-8.5,-8,-8,-8,-7.5,-7.5,-7.5)\ntheta &lt;- c(0.6438,0.6365,0.6090,0.2698,0.2182,0.2342,0.0750,0.0787,0.0612)\nresult &lt;- nls(theta~1&#47;(1+exp(a*log(10)*(logIT - logIC50))),start = c(logIC50=-8.5, a=1))\nsummary(result)\n<\/pre>\n<p><b>Output<\/b>:<\/p>\n<pre class=\"prettyprint\">\nFormula: theta ~ 1&#47;(1 + exp(a * log(10) * (logIT - logIC50)))\n\nParameters:\n        Estimate Std. Error t value Pr(&gt;|t|)    \nlogIC50 -8.34075    0.01186 -703.26  &lt; 2e-16 ***\na        1.41699    0.05829   24.31 5.08e-08 ***\n---\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n\nResidual standard error: 0.01991 on 7 degrees of freedom\n\nNumber of iterations to convergence: 5 \nAchieved convergence tolerance: 8.394e-06\n<\/pre>\n<pre class=\"prettyprint\">confint(result, level=0.95)\n<\/pre>\n<p><b>Output<\/b>:<\/p>\n<pre class=\"prettyprint\">\n             2.5%     97.5%\nlogIC50 -8.369216 -8.313125\na        1.282066  1.563688\n<\/pre>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"991\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/ligand_sigmoid-1024x991.png\" alt=\"\" class=\"wp-image-6677\" style=\"aspect-ratio:1.0333096276933131;width:410px;height:auto\" srcset=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/ligand_sigmoid-1024x991.png 1024w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/ligand_sigmoid-300x290.png 300w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/ligand_sigmoid-768x744.png 768w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/ligand_sigmoid.png 1444w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">log IC<sub>50<\/sub> = -8.341\u3068\u63a8\u5b9a\u3055\u308c\u305f\u3002nM\u306b\u5909\u63db\u3059\u308b\u30684.560 nM\u3002<\/figcaption><\/figure>\n<\/div>\n\n\n<p>\u63a8\u5b9aIC<sub>50<\/sub>\u5024\u306f4.560 nM\uff0895%CI: 4.274\u20134.863\uff09\u3001\u30d2\u30eb\u4fc2\u6570\u306f1.417\u3060\u3063\u305f\u3002<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><em>K<\/em><sub>i<\/sub>\u3078\u306e\u5909\u63db<\/h5>\n\n\n\n<p>\u4ee5\u4e0b\u306e\u5f0f\u3067\u63a8\u5b9a\u3057\u305f\\(\\mathrm{IC}_{50}\\)\u3092\\(K_\\mathrm{i}\\) \u306b\u5909\u63db\u3059\u308b\u3002<\/p>\n\n\n\n<p>$$ K_{\\rm i} = \\frac{\\frac{1}{1 + k} \\left[\\mathrm{IC}_{50} - \\left( 1 - \\frac{1}{2} \\frac{[L]_0}{[L]_{50}} \\right)[R]_{\\mathrm{T}} - \\left( \\frac{[L]_0}{[L]_{50}} - 1\\right) \\frac{[RL]_{0}}{2} \\right] }{2\\frac{[L]_{50}}{[L]_0} - 1 + \\frac{[L]_{50}}{K_{\\rm d}}} $$<\/p>\n\n\n\n<p>\u5f97\u3089\u308c\u305f\\(K_\\mathrm{i}\\)  \u306f <strong>0.0561 nM<\/strong>\uff0895% CI: 0.0471\u20130.0656\uff09\u3060\u3063\u305f\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">log<sub>10<\/sub> {<em>\u03b8<\/em>\/(1 \u2212 <em>\u03b8<\/em>)} \u5909\u63db\u304b\u3089\u7dda\u5f62\u56de\u5e30\u3067IC<sub>50<\/sub>\u3092\u63a8\u5b9a\u3014\u6b21\u306b\u63a8\u5968 \u203bMicrosoft Excel\u3057\u304b\u4f7f\u3048\u306a\u3044\u6642\u3015<\/h4>\n\n\n\n<pre class=\"prettyprint\">logIT &lt;- c(-8.5,-8.5,-8.5,-8,-8,-8,-7.5,-7.5,-7.5)\nlogit &lt;- c(0.257,0.243,0.193,-0.432,-0.554,-0.515,-1.091,-1.068,-1.186)\nresult_lm &lt;- lm(logit ~ logIT)\nsummary(result_lm)\n<\/pre>\n<p><b>Output<\/b>:<\/p>\n<pre class=\"prettyprint\">\nCall:\nlm(formula = logit ~ logIT)\n\nResiduals:\n     Min       1Q   Median       3Q      Max \n-0.09256 -0.05156  0.02944  0.04344  0.06644 \n\nCoefficients:\n             Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) -11.22944    0.38820  -28.93 1.52e-08 ***\nlogIT        -1.34600    0.04846  -27.77 2.01e-08 ***\n---\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n\nResidual standard error: 0.05935 on 7 degrees of freedom\nMultiple R-squared:  0.991,\tAdjusted R-squared:  0.9897 \nF-statistic: 771.4 on 1 and 7 DF,  p-value: 2.014e-08\n<\/pre>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"976\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/ligand_linear-1024x976.png\" alt=\"\" class=\"wp-image-6678\" style=\"width:409px;height:auto\" srcset=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/ligand_linear-1024x976.png 1024w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/ligand_linear-300x286.png 300w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/ligand_linear-768x732.png 768w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/ligand_linear.png 1438w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">\\( y = -1.34600 x - 11.22944\\). \\(R^2 = 0.991\\). <br>log<sub>10<\/sub> IC<sub>50<\/sub> = -11.22944\/1.34600 = -8.342823\u3002nM\u306b\u5909\u63db\u3059\u308b\u30684.541 nM\u3002<\/figcaption><\/figure>\n<\/div>\n\n\n<p>\u63a8\u5b9aIC<sub>50<\/sub>\u5024\u306f4.541 nM\u3001\u524d\u7bc0\u3068\u540c\u3058\u5f0f\u3067\u5909\u63db\u3057\u305f<em>K<\/em><sub>i<\/sub>\u5024\u306f<strong>0.0555 nM<\/strong>\u3060\u3063\u305f\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">GraphPad Prism\u306e\u65b9\u6cd5<\/h4>\n\n\n\n<h5 class=\"wp-block-heading\">\u30d1\u30e9\u30e1\u30fc\u30bf<\/h5>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>Hot<\/em> = [<em>L<\/em>]<sub>T<\/sub> = 18.74 [nM] = 128050 [DPM]<\/li>\n\n\n\n<li><em>KdNM<\/em> = <em>K<\/em><sub>d<\/sub> = 0.53 [nM]<\/li>\n\n\n\n<li><em>SpAct<\/em> = 12.31 [Ci\/mmol] = 27.3282 [dpm\/fmol]<\/li>\n\n\n\n<li><em>Vol<\/em> = 0.25 [mL]<\/li>\n<\/ul>\n\n\n\n<pre class=\"prettyprint lang-r\">X &lt;- c(-8.5, -8.5, -8.5, -8, -8, -8, -7.5, -7.5, -7.5)\nY &lt;- c(26327, 26072, 25105, 13168, 11354, 11917, 6314, 6446, 5829)\nHot &lt;- 128050\nKdNM &lt;- 0.53\nSpAct &lt;- 27.3282\nVol &lt;- 0.25\nbinding_model &lt;- function(X, LogKi, Bmax, NS, Hot, KdNM, SpAct, Vol) {\n      KdDPM &lt;- KdNM * SpAct * Vol * 1000\n      R &lt;- 1 + NS\n      S &lt;- (1 + 10^(X - LogKi)) * KdDPM + Hot\n      a &lt;- -R\n      b &lt;- R * S + NS * Hot + Bmax\n      c &lt;- -Hot * (S * NS + Bmax)\n      return((-b + sqrt(b^2 - 4 * a * c)) &#47; (2 * a))\n}\nresult_GP &lt;- nls(\n     Y ~ binding_model(X, LogKi, Bmax, NS, Hot, KdNM, SpAct, Vol),\n     start = list(\n         LogKi = -8.0, \n         Bmax  = 30000,\n         NS    = 0.03\n     ),\n     algorithm = &#34;port&#34;\n)\nsummary(result_GP)\n<\/pre>\n<p><b>Output<\/b>:<\/p>\n<pre class=\"prettyprint\">\nFormula: Y ~ binding_model(X, LogKi, Bmax, NS, Hot, KdNM, SpAct, Vol)\n\nParameters:\n        Estimate Std. Error t value Pr(&gt;|t|)    \nLogKi -1.069e+01  3.972e-01 -26.903 1.74e-07 ***\nBmax   1.510e+05  1.131e+05   1.335   0.2304    \nNS     2.424e-02  6.612e-03   3.667   0.0105 *  \n---\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n\nResidual standard error: 679 on 6 degrees of freedom\n\nAlgorithm &#34;port&#34;, convergence message: both X-convergence and relative convergence (5)\n<\/pre>\n\n\n\n<p>\u7d50\u679c\u306f <em>K<\/em><sub>i<\/sub> = 10^(-10.69 + 9) = 0.0204 [nM]\u3001Bmax = 151,000\u3001NS = 0.02424\u3002<em>K<\/em><sub>i<\/sub>\u306f\u5c0f\u3055\u904e\u304e\u3001Bmax\uff08= [<em>R<\/em>]<sub>T<\/sub>\uff09\u306f\u5927\u304d\u904e\u304e\u308b\u3002<\/p>\n\n\n\n<p>\u53ef\u8996\u5316:<\/p>\n\n\n\n<pre class=\"prettyprint\">concpre = seq(-9.5,-3.5, length=100)\nplot(Y~X,xlim=c(-10,-3.5),ylim=c(0,50000))\nlines(concpre, predict(result_GP, newdata=list(X=concpre)))\n<\/pre>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"961\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/GraphPad_XY-1024x961.png\" alt=\"\" class=\"wp-image-6770\" style=\"aspect-ratio:1.0655672718623643;width:405px;height:auto\" srcset=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/GraphPad_XY-1024x961.png 1024w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/GraphPad_XY-300x281.png 300w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/GraphPad_XY-768x720.png 768w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2016\/11\/GraphPad_XY.png 1454w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>In the world of drug discovery 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